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The Work of Stephen Hawking in Physical Review

To mark the passing of Stephen Hawking, we gathered together his 55 papers in Physical Review D and Physical Review Letters . They probe the edges of space and time, from "Black holes and thermodynamics” to "Wave function of the Universe."

85 citations

Occurrence of singularities in open universes, s. w. hawking, phys. rev. lett. 15 , 689 (1965) – published 25 october 1965, 94 citations, singularities in the universe, phys. rev. lett. 17 , 444 (1966) – published 22 august 1966, 738 citations, gravitational radiation from colliding black holes, phys. rev. lett. 26 , 1344 (1971) – published 24 may 1971, 50 citations, theory of the detection of short bursts of gravitational radiation, g. w. gibbons and s. w. hawking, phys. rev. d 4 , 2191 (1971) – published 15 october 1971, 958 citations, black holes and thermodynamics, phys. rev. d 13 , 191 (1976) – published 15 january 1976, 757 citations, path-integral derivation of black-hole radiance, j. b. hartle and s. w. hawking, phys. rev. d 13 , 2188 (1976) – published 15 april 1976, 1,507 citations, breakdown of predictability in gravitational collapse, phys. rev. d 14 , 2460 (1976) – published 15 november 1976, 2,179 citations, cosmological event horizons, thermodynamics, and particle creation, phys. rev. d 15 , 2738 (1977) – published 15 may 1977, 2,185 citations, action integrals and partition functions in quantum gravity, phys. rev. d 15 , 2752 (1977) – published 15 may 1977, 105 citations, quantum gravity and path integrals, phys. rev. d 18 , 1747 (1978) – published 15 september 1978, 394 citations, bubble collisions in the very early universe, s. w. hawking, i. g. moss, and j. m. stewart, phys. rev. d 26 , 2681 (1982) – published 15 november 1982, milestone 1,974 citations, wave function of the universe, phys. rev. d 28 , 2960 (1983) – published 15 december 1983, 468 citations, origin of structure in the universe, j. j. halliwell and s. w. hawking, phys. rev. d 31 , 1777 (1985) – published 15 april 1985, 134 citations, arrow of time in cosmology, phys. rev. d 32 , 2489 (1985) – published 15 november 1985, 300 citations, wormholes in spacetime, phys. rev. d 37 , 904 (1988) – published 15 february 1988, 113 citations, spectrum of wormholes, s. w. hawking and don n. page, phys. rev. d 42 , 2655 (1990) – published 15 october 1990, 16 citations, wormholes in string theory, alex lyons and s. w. hawking, phys. rev. d 44 , 3802 (1991) – published 15 december 1991, 506 citations, chronology protection conjecture, phys. rev. d 46 , 603 (1992) – published 15 july 1992, 89 citations, evaporation of two-dimensional black holes, phys. rev. lett. 69 , 406 (1992) – published 20 july 1992, 36 citations, kinks and topology change, phys. rev. lett. 69 , 1719 (1992) – published 21 september 1992, 51 citations, origin of time asymmetry, s. w. hawking, r. laflamme, and g. w. lyons, phys. rev. d 47 , 5342 (1993) – published 15 june 1993, 7 citations, quantum coherence in two dimensions, s. w. hawking and j. d. hayward, phys. rev. d 49 , 5252 (1994) – published 15 may 1994, 5 citations, superscattering matrix for two-dimensional black holes, phys. rev. d 50 , 3982 (1994) – published 15 september 1994, 305 citations, entropy, area, and black hole pairs, s. w. hawking, gary t. horowitz, and simon f. ross, phys. rev. d 51 , 4302 (1995) – published 15 april 1995, 71 citations, pair production of black holes on cosmic strings, s. w. hawking and simon f. ross, phys. rev. lett. 75 , 3382 (1995) – published 6 november 1995, 69 citations, probability for primordial black holes, r. bousso and s. w. hawking, phys. rev. d 52 , 5659 (1995) – published 15 november 1995, 39 citations, quantum coherence and closed timelike curves, phys. rev. d 52 , 5681 (1995) – published 15 november 1995, 157 citations, duality between electric and magnetic black holes, phys. rev. d 52 , 5865 (1995) – published 15 november 1995, 74 citations, virtual black holes, phys. rev. d 53 , 3099 (1996) – published 15 march 1996, 176 citations, pair creation of black holes during inflation, raphael bousso and stephen w. hawking, phys. rev. d 54 , 6312 (1996) – published 15 november 1996, 17 citations, evolution of near-extremal black holes, s. w. hawking and m. m. taylor-robinson, phys. rev. d 55 , 7680 (1997) – published 15 june 1997, 26 citations, loss of quantum coherence through scattering off virtual black holes, phys. rev. d 56 , 6403 (1997) – published 15 november 1997, 59 citations, trace anomaly of dilaton-coupled scalars in two dimensions, raphael bousso and stephen hawking, phys. rev. d 56 , 7788 (1997) – published 15 december 1997, 25 citations, models for chronology selection, m. j. cassidy and s. w. hawking, phys. rev. d 57 , 2372 (1998) – published 15 february 1998, 136 citations, (anti-)evaporation of schwarzschild–de sitter black holes, phys. rev. d 57 , 2436 (1998) – published 15 february 1998, 18 citations, bulk charges in eleven dimensions, phys. rev. d 58 , 025006 (1998) – published 12 june 1998, 15 citations, inflation, singular instantons, and eleven dimensional cosmology, s. w. hawking and harvey s. reall, phys. rev. d 59 , 023502 (1998) – published 7 december 1998, 114 citations, gravitational entropy and global structure, s. w. hawking and c. j. hunter, phys. rev. d 59 , 044025 (1999) – published 26 january 1999, 164 citations, nut charge, anti–de sitter space, and entropy, s. w. hawking, c. j. hunter, and don n. page, phys. rev. d 59 , 044033 (1999) – published 28 january 1999, 416 citations, rotation and the ads-cft correspondence, s. w. hawking, c. j. hunter, and m. m. taylor-robinson, phys. rev. d 59 , 064005 (1999) – published 1 february 1999, 23 citations, lorentzian condition in quantum gravity, phys. rev. d 59 , 103501 (1999) – published 29 march 1999, 166 citations, charged and rotating ads black holes and their cft duals, s. w. hawking and h. s. reall, phys. rev. d 61 , 024014 (1999) – published 20 december 1999, 355 citations, brane-world black holes, a. chamblin, s. w. hawking, and h. s. reall, phys. rev. d 61 , 065007 (2000) – published 25 february 2000, 197 citations, brane new world, s. w. hawking, t. hertog, and h. s. reall, phys. rev. d 62 , 043501 (2000) – published 29 june 2000, 52 citations, gravitational waves in open de sitter space, s. w. hawking, thomas hertog, and neil turok, phys. rev. d 62 , 063502 (2000) – published 31 july 2000, 129 citations, trace anomaly driven inflation, phys. rev. d 63 , 083504 (2001) – published 5 march 2001, 200 citations, living with ghosts, s. w. hawking and thomas hertog, phys. rev. d 65 , 103515 (2002) – published 9 may 2002, 28 citations, why does inflation start at the top of the hill, phys. rev. d 66 , 123509 (2002) – published 20 december 2002, 271 citations, information loss in black holes, phys. rev. d 72 , 084013 (2005) – published 18 october 2005, 45 citations, populating the landscape: a top-down approach, phys. rev. d 73 , 123527 (2006) – published 23 june 2006, no-boundary measure of the universe, james b. hartle, s. w. hawking, and thomas hertog, phys. rev. lett. 100 , 201301 (2008) – published 23 may 2008, 118 citations, classical universes of the no-boundary quantum state, phys. rev. d 77 , 123537 (2008) – published 25 june 2008, 33 citations, no-boundary measure in the regime of eternal inflation, james hartle, s. w. hawking, and thomas hertog, phys. rev. d 82 , 063510 (2010) – published 8 september 2010, 35 citations, local observation in eternal inflation, phys. rev. lett. 106 , 141302 (2011) – published 8 april 2011, featured in physics editors' suggestion 488 citations, soft hair on black holes, stephen w. hawking, malcolm j. perry, and andrew strominger, phys. rev. lett. 116 , 231301 (2016) – published 6 june 2016.

A black hole may carry “soft hair,” low-energy quantum excitations that release information when the black hole evaporates.

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Read 55 of Stephen Hawking’s Research Papers for Free

Read Hawking's takes on black holes and string theory.

Over the course of his life, famed physicist Stephen Hawking wrote dozens of papers that explored the mysteries of time and space. From his 1966 thesis onward, he helped revolutionize the field of astrophysics and define what we know about the universe by diving into topics like string theory, black holes, and the Big Bang .

In the wake of his death last week, the American Physical Society (APS) has released 55 of his studies to “mark the passing of Stephen Hawking.” You can read them here . To fully understand the gravity of what’s going on here, you may want to brush up on your physics: There’s a reason Hawking is considered one of our preeminent geniuses. A huge number of them deal with wormholes and black holes , including this banger on black hole “soft hair,” or zero-energy particles that store information from the stars black holes gobble up.

Hawking helped confirm that black holes are birthed when a star collapses.

These 55 papers are found in the journals Physical Review D and Physical Review Letters , which are published by the APS. These studies, published from 1965 to 2016, the APS states on its site, “probe the edges of space and time.” The first paper published here, “Occurrence of Singularities in Open Universes,” was written a year before his infamous 1966 thesis on expanding universes and marks the start of his work that deals with the universe beginning from a singularity .

Some of the papers also are also an exercise in some fanciful titling by Hawking and his coauthors, including “ Brane New World ” and “ Living With Ghosts .” The latter deals with how gravitational dimensions affect ghost states — which are unphysical states on the wrong side of the kinetic term , and not actually ghosts .

When you’re done with the classics, you can move on over to a new hit titled “A Smooth Exit from Eternal Inflation?” This final paper from Hawking, co-authored with theoretical physicist Thomas Hertog, Ph.D., was submitted two weeks before Hawking’s death and currently exists in its preprint form .

While it doesn’t exactly predict the end of the universe, (something Hawking liked to discuss on in his free time), it does propose a new way to detect the ‘multiverse’: a mathematical road other scientists can explore, ensuring Hawking’s work lives on in the future.

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Stephen Hawking's final scientific paper released

Black Hole Entropy and Soft Hair was completed in the days before the physicist’s death in March

Black holes and soft hair: why Stephen Hawking’s final work is important

Stephen Hawking’s final scientific paper has been released by physicists who worked with the late cosmologist on his career-long effort to understand what happens to information when objects fall into black holes.

The work, which tackles what theoretical physicists call “the information paradox”, was completed in the days before Hawking’s death in March . It has now been written up by his colleagues at Cambridge and Harvard universities and posted online .

Malcolm Perry, a professor of theoretical physics at Cambridge and a co-author on the paper, Black Hole Entropy and Soft Hair, said the information paradox was “at the centre of Hawking’s life” for more than 40 years.

The origins of the puzzle can be traced back to Albert Einstein. In 1915, Einstein published his theory of general relativity, a tour-de-force that described how gravity arises from the spacetime-bending effects of matter, and so why the planets circle the sun. But Einstein’s theory made important predictions about black holes too, notably that a black hole can be completely defined by only three features: its mass, charge, and spin.

Nearly 60 years later, Hawking added to the picture. He argued that black holes also have a temperature. And because hot objects lose heat into space, the ultimate fate of a black hole is to evaporate out of existence. But this throws up a problem. The rules of the quantum world demand that information is never lost. So what happens to all the information contained in an object – the nature of a moon’s atoms, for instance – when it tumbles into a black hole?

“The difficulty is that if you throw something into a black hole it looks like it disappears,” said Perry. “How could the information in that object ever be recovered if the black hole then disappears itself?”

In the latest paper, Hawking and his colleagues show how some information at least may be preserved. Toss an object into a black hole and the black hole’s temperature ought to change. So too will a property called entropy, a measure of an object’s internal disorder, which rises the hotter it gets.

The physicists, including Sasha Haco at Cambridge and Andrew Strominger at Harvard, show that a black hole’s entropy may be recorded by photons that surround the black hole’s event horizon, the point at which light cannot escape the intense gravitational pull. They call this sheen of photons “soft hair”.

“What this paper does is show that ‘soft hair’ can account for the entropy,” said Perry. “It’s telling you that soft hair really is doing the right stuff.”

It is not the end of the information paradox though. “We don’t know that Hawking entropy accounts for everything you could possibly throw at a black hole, so this is really a step along the way,” said Perry. “We think it’s a pretty good step, but there is a lot more work to be done.”

Days before Hawking died, Perry was at Harvard working on the paper with Strominger. He was not aware how ill Hawking was and called to give the physicist an update. It may have been the last scientific exchange Hawking had. “It was very difficult for Stephen to communicate and I was put on a loudspeaker to explain where we had got to. When I explained it, he simply produced an enormous smile. I told him we’d got somewhere. He knew the final result.”

Among the unknowns that Perry and his colleagues must now explore are how information associated with entropy is physically stored in soft hair and how that information comes out of a black hole when it evaporates.

“If I throw something in, is all of the information about what it is stored on the black hole’s horizon?” said Perry. “That is what is required to solve the information paradox. If it’s only half of it, or 99%, that is not enough, you have not solved the information paradox problem.

“It’s a step on the way, but it is definitely not the entire answer. We have slightly fewer puzzles than we had before, but there are definitely some perplexing issues left.”

Marika Taylor, professor of theoretical physics at Southampton University and a former student of Hawking’s, said: “Understanding the microscopic origin of this entropy – what are the underlying quantum states that the entropy counts? – has been one of the great challenges of the last 40 years.

“This paper proposes a way to understand entropy for astrophysical black holes based on symmetries of the event horizon. The authors have to make several non-trivial assumptions so the next steps will be to show that these assumptions are valid.”

Juan Maldacena, a theoretical physicist at Einstein’s alma mater, the Institute for Advanced Studies in Princeton, said: “Hawking found that black holes have a temperature. For ordinary objects we understand temperature as due to the motion of the microscopic constituents of the system. For example, the temperature of air is due to the motion of the molecules: the faster they move, the hotter it is.

“For black holes, it is unclear what those constituents are, and whether they can be associated to the horizon of a black hole. In some physical systems that have special symmetries, the thermal properties can be calculated in terms of these symmetries. This paper shows that near the black hole horizon we have one of these special symmetries.”

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Physicists observationally confirm Hawking’s black hole theorem for the first time

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There are certain rules that even the most extreme objects in the universe must obey. A central law for black holes predicts that the area of their event horizons — the boundary beyond which nothing can ever escape — should never shrink. This law is Hawking’s area theorem, named after physicist Stephen Hawking, who derived the theorem in 1971.

Fifty years later, physicists at MIT and elsewhere have now confirmed Hawking’s area theorem for the first time, using observations of gravitational waves. Their results appear today in Physical Review Letters .

In the study, the researchers take a closer look at GW150914, the first gravitational wave signal detected by the Laser Interferometer Gravitational-wave Observatory (LIGO), in 2015. The signal was a product of two inspiraling black holes that generated a new black hole, along with a huge amount of energy that rippled across space-time as gravitational waves.

If Hawking’s area theorem holds, then the horizon area of the new black hole should not be smaller than the total horizon area of its parent black holes. In the new study, the physicists reanalyzed the signal from GW150914 before and after the cosmic collision and found that indeed, the total event horizon area did not decrease after the merger — a result that they report with 95 percent confidence.

Their findings mark the first direct observational confirmation of Hawking’s area theorem, which has been proven mathematically but never observed in nature until now. The team plans to test future gravitational-wave signals to see if they might further confirm Hawking’s theorem or be a sign of new, law-bending physics.

“It is possible that there’s a zoo of different compact objects, and while some of them are the black holes that follow Einstein and Hawking’s laws, others may be slightly different beasts,” says lead author Maximiliano Isi, a NASA Einstein Postdoctoral Fellow in MIT’s Kavli Institute for Astrophysics and Space Research. “So, it’s not like you do this test once and it’s over. You do this once, and it’s the beginning.”

Isi’s co-authors on the paper are Will Farr of Stony Brook University and the Flatiron Institute’s Center for Computational Astrophysics, Matthew Giesler of Cornell University, Mark Scheel of Caltech, and Saul Teukolsky of Cornell University and Caltech.

An age of insights

In 1971, Stephen Hawking proposed the area theorem, which set off a series of fundamental insights about black hole mechanics. The theorem predicts that the total area of a black hole’s event horizon — and all black holes in the universe, for that matter — should never decrease. The statement was a curious parallel of the second law of thermodynamics, which states that the entropy, or degree of disorder within an object, should also never decrease.

The similarity between the two theories suggested that black holes could behave as thermal, heat-emitting objects — a confounding proposition, as black holes by their very nature were thought to never let energy escape, or radiate. Hawking eventually squared the two ideas in 1974, showing that black holes could have entropy and emit radiation over very long timescales if their quantum effects were taken into account. This phenomenon was dubbed “Hawking radiation” and remains one of the most fundamental revelations about black holes.

“It all started with Hawking’s realization that the total horizon area in black holes can never go down,” Isi says. “The area law encapsulates a golden age in the ’70s where all these insights were being produced.”

Hawking and others have since shown that the area theorem works out mathematically, but there had been no way to check it against nature until LIGO’s first detection of gravitational waves .

Hawking, on hearing of the result, quickly contacted LIGO co-founder Kip Thorne, the Feynman Professor of Theoretical Physics at Caltech. His question: Could the detection confirm the area theorem?

At the time, researchers did not have the ability to pick out the necessary information within the signal, before and after the merger, to determine whether the final horizon area did not decrease, as Hawking’s theorem would assume. It wasn’t until several years later, and the development of a technique by Isi and his colleagues, when testing the area law became feasible.

Before and after

In 2019, Isi and his colleagues developed a technique to extract the reverberations immediately following GW150914’s peak — the moment when the two parent black holes collided to form a new black hole. The team used the technique to pick out specific frequencies, or tones of the otherwise noisy aftermath, that they could use to calculate the final black hole’s mass and spin.

A black hole’s mass and spin are directly related to the area of its event horizon, and Thorne, recalling Hawking’s query, approached them with a follow-up: Could they use the same technique to compare the signal before and after the merger, and confirm the area theorem?

The researchers took on the challenge, and again split the GW150914 signal at its peak. They developed a model to analyze the signal before the peak, corresponding to the two inspiraling black holes, and to identify the mass and spin of both black holes before they merged. From these estimates, they calculated their total horizon areas — an estimate roughly equal to about 235,000 square kilometers, or roughly nine times the area of Massachusetts.

They then used their previous technique to extract the “ringdown,” or reverberations of the newly formed black hole, from which they calculated its mass and spin, and ultimately its horizon area, which they found was equivalent to 367,000 square kilometers (approximately 13 times the Bay State’s area).

“The data show with overwhelming confidence that the horizon area increased after the merger, and that the area law is satisfied with very high probability,” Isi says. “It was a relief that our result does agree with the paradigm that we expect, and does confirm our understanding of these complicated black hole mergers.”

The team plans to further test Hawking’s area theorem, and other longstanding theories of black hole mechanics, using data from LIGO and Virgo, its counterpart in Italy.

“It’s encouraging that we can think in new, creative ways about gravitational-wave data, and reach questions we thought we couldn’t before,” Isi says. “We can keep teasing out pieces of information that speak directly to the pillars of what we think we understand. One day, this data may reveal something we didn’t expect.”

This research was supported, in part, by NASA, the Simons Foundation, and the National Science Foundation.

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Researchers from MIT and other institutions have been able to observationally confirm one of Stephen Hawking’s theorems about black holes, measuring gravitational waves before and after a black hole merger to provide evidence that a black hole’s event horizon can never shrink, reports Caroline Delbert for Popular Mechanics . “This cool analysis doesn't just show an example of Hawking's theorem that underpins one of the central laws affecting black holes,” writes Delbert, “it shows how analyzing gravitational wave patterns can bear out statistical findings.”

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Physical Review D

Covering particles, fields, gravitation, and cosmology, collections.

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Wormholes in spacetime

S. w. hawking, phys. rev. d 37 , 904 – published 15 february 1988, an article within the collection: the work of stephen hawking in physical review.

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Any reasonable theory of quantum gravity will allow closed universes to branch off from our nearly flat region of spacetime. I describe the possible quantum states of these closed universes. They correspond to wormholes which connect two asymptotically Euclidean regions, or two parts of the same asymptotically Euclidean region. I calculate the influence of these wormholes on ordinary quantum fields at low energies in the asymptotic region. This can be represented by adding effective interactions in flat spacetime which create or annihilate closed universes containing certain numbers of particles. The effective interactions are small except for closed universes containing scalar particles in the spatially homogeneous mode. If these scalar interactions are not reduced by sypersymmetry, it may be that any scalar particles we observe would have to be bound states of particles of higher spin, such as the pion. An observer in the asymptotically flat region would not be able to measure the quantum state of closed universes that branched off. He would therefore have to sum over all possibilities for the closed universes. This would mean that the final state would appear to be a mixed quantum state, rather than a pure quantum state.

• Received 28 October 1987

DOI: https://doi.org/10.1103/PhysRevD.37.904

©1988 American Physical Society

This article appears in the following collection:

The Work of Stephen Hawking in Physical Review

To mark the passing of Stephen Hawking, we gathered together his 55 papers in Physical Review D and Physical Review Letters . They probe the edges of space and time, from "Black holes and thermodynamics” to "Wave function of the Universe."

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• Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Silver Street, Cambridge CB3 9EW, England

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Stephen Hawking: Three publications that shaped his career

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A pop culture icon and ground-breaking physicist, Stephen Hawking is one of the most prominent figures in modern science. Nature Video explores three of the publications that shaped his career and his legacy.

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Stephen Hawking’s Final Paper: How to Escape From a Black Hole

In a study from beyond the grave, the theoretical physicist sings (mathematically) of memory, loss and the possibility of data redemption.

By Dennis Overbye

The cosmologist and pop-science icon Stephen Hawking, who died last March on Einstein’s birthday, spoke out from the grave recently in the form of his last scientific paper . Appropriately for a man on the Other Side, the paper is about how to escape from a black hole.

Cleansed of its abstract mathematics, the paper is an ode to memory, loss and the oldest of human yearnings, the desire for transcendence. As the doomed figure in Bruce Springsteen’s “Atlantic City” sings, “Everything dies, baby, that’s a fact, but maybe everything that dies someday comes back.”

Dr. Hawking was the manifestation of perseverance; stricken by Lou Gehrig’s disease, he managed to conquer the universe from a wheelchair. The fate of matter or information caught in a black hole is one that defined his career, and it has become one of the deepest issues in physics.

Black holes are objects so dense that, according to Einstein’s law of general relativity, not even light can escape. In 1974, Dr. Hawking turned these objects, and the rest of physics, inside-out. He discovered, to his surprise, that the random quantum effects that rule the microscopic world would cause black holes to leak and, eventually, explode and disappear.

In the fullness of time (which in many cases would be longer than the current age of the universe), all the mass and energy that had fallen into the hole would come back out. But, according to the classical Einstein equations, black holes are disturbingly simple; their only properties are mass, electrical charge and angular momentum. Every other detail about what falls into a black hole disappears from the universe’s memory banks. A black hole has no complications — no hair — the saying went.

So the fountain of matter and energy exiting a black hole would be random, Dr. Hawking emphasized in a paper in 1975. If you fell into one and came back out, you would lack all the details that had made you: male or female, blue eyes or brown, Yankee fan or Red Sox fan. The equation describing that fate is inscribed on Dr. Hawking’s tombstone, in Westminster Abbey, where it presumably will endure the ages.

That’s some kind of reincarnation. If nature can forget you, it could forget anything — a deathblow to the ability of science to reconstruct the past or predict the future. “It’s the past that tells us who we are,” Dr. Hawking told a conference at Harvard a couple years ago. “Without it, we lose our identity.”

In effect, Dr. Hawking maintained in his 1975 paper, the paradoxical quantum effects that Einstein had once dismissed, saying that God doesn’t play dice, were adding an extra forgetfulness to nature. “God not only plays dice,” Dr. Hawking wrote, “but he often throws them where they can’t be seen.”

Those were fighting words to other physicists; it was a basic tenet that the proverbial film of history can be run backward, to reconstruct what happened in, say, the collision of a pair of subatomic particles in a high-energy collider.

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Thirty years later Dr. Hawking recanted , but the argument went on. The “information paradox,” as it is known, remained at the center of physics because nobody, not even Dr. Hawking, could explain how black holes actually process the information that enters or exits them.

But scientists have been having a blast theorizing about the nature of space-time, information and memory. Some have suggested that you can’t even get into a black hole without being vaporized by a firewall of energy, let alone get back out.

Recent years have brought a glimmer of hope. Andrew Strominger of Harvard discovered that, when viewed from the right mathematical perspective — that of a light ray headed toward the infinite future — black holes are more complicated than we thought. They have what Dr. Strominger has called “soft hair,” in the form of those imaginary light rays, which can be ruffled, stroked, twisted and otherwise arranged by material coming into the black hole. In principle, this hair could encode information on the surface of the black hole, recording all those details that Einstein’s equations supposedly leave out .

Whether this is enough to save physics, let alone a person falling into a black hole, is what Dr. Hawking was working on in the years before he died.

“When I wrote my paper 40 years ago, I thought the information would pass into another universe,” he told me at the Harvard conference. Now, he said, it’s on the surface of the black hole. “The information will be re-emitted when the black hole evaporates.”

An Earthling’s Guide to Black Holes

Welcome to the place of no return — a region in space where the gravitational pull is so strong that not even light can escape it. This is a black hole.

Other experts, including Juan Maldacena of the Institute for Advanced Study in Princeton, have been more measured, saying that if soft hair does not solve the information paradox, it might at least help.

In his recent, posthumous report, which drew a flurry of press , Dr. Hawking and his colleagues endeavored to show how this optimistic idea could work. Besides Dr. Hawking, the paper’s authors were Dr. Strominger as well as Malcolm Perry and Sasha Haco of Cambridge University.

Dr. Strominger is hopeful that physicists one day will be able to understand black holes just by reading what is written in this soft hair.

“We didn’t prove it,” he said in an email. But, he added, they did succeed in showing how all the pieces could fit together: “If our guess is right, this paper will be of central importance. If not, it will be a technical footnote.”

Few of us, including Dr. Hawking, ever harbored the hope that solving the information paradox would bring back our parents, the dinosaurs or Joe DiMaggio from whatever was waiting in Atlantic City. Somewhere along the way we’ve all made some sort of accommodation with the idea that our personal timelines will come to an end, but we take some comfort in knowing that we will be remembered, and that our genes and books and names will carry on.

Last year’s Pixar/Disney movie “Coco,” which I happened to watch with my daughter recently, tells the story of a young Mexican boy who visits the Land of the Dead to find an ancestor who can help him in his quest to become a musician. The Land of the Dead is a lively place, but its denizens can only stay there, it turns out, as long as someone remembers them . When the memories vanish, so even do the animated skeletons

Some astronomers now say that even this pale version of salvation might be in jeopardy . A mysterious force called dark energy is speeding up the expansion of the universe. Someday, these experts say, if the expansion continues, making the galaxies fly away faster and faster, the rest of the universe will be permanently out of sight to us, and we will be forever out of sight of it. It would be as if we were surrounded by a black hole, into which all our information and memory were disappearing.

In our little bubble of the Milky Way, we might always remember Aretha and Cleopatra and Shakespeare and Hawking. But will the rest of the universe remember us?

Dennis Overbye joined The Times in 1998, and has been a reporter since 2001. He has written two books: “Lonely Hearts of the Cosmos: The Story of the Scientific Search for the Secret of the Universe” and “Einstein in Love: A Scientific Romance.” More about Dennis Overbye

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We finally know why Stephen Hawking's black hole equation works

Stephen Hawking and Jacob Bekenstein calculated the entropy of a black hole in the 1970s, but it took physicists until now to figure out the quantum effects that make the formula work

By Leah Crane

5 April 2024

An artist’s visualisation of a black hole

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We finally understand how black holes get their entropy. Physicists have been struggling to figure this out since the early 1970s, when Stephen Hawking and Jacob Bekenstein calculated how much entropy, or disorder, should be present in a black hole. Now, with a little help from quantum mechanics, researchers may have finally solved the problem.

“For a long time, people have thought that to solve this problem, you have to do all kinds of fancy things in string theory. But what we show is…

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High Energy Physics - Theory

Title: black hole entropy and soft hair.

Abstract: A set of infinitesimal ${\rm Virasoro_{\,L}}\otimes{\rm Virasoro_{\,R}}$ diffeomorphisms are presented which act non-trivially on the horizon of a generic Kerr black hole with spin J. The covariant phase space formalism provides a formula for the Virasoro charges as surface integrals on the horizon. Integrability and associativity of the charge algebra are shown to require the inclusion of `Wald-Zoupas' counterterms. A counterterm satisfying the known consistency requirement is constructed and yields central charges $c_L=c_R=12J$. Assuming the existence of a quantum Hilbert space on which these charges generate the symmetries, as well as the applicability of the Cardy formula, the central charges reproduce the macroscopic area-entropy law for generic Kerr black holes.

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Stephen Hawking’s final paper predicted the end of the world and revealed a parallel universe

STEPHEN Hawking submitted a research paper just weeks before he died hinting how scientists could find another universe.

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PROFESSOR Stephen Hawking submitted a research paper just two weeks before he died hinting how scientists could find another universe and predicting the end of the world.

The iconic physicist completed the groundbreaking research from his deathbed, said co-author professor Thomas Hertog.

It sets out the maths needed for a Star Trek-style space probe to find experimental evidence for the existence of a “multiverse” — the idea our cosmos is only one of many universes.

If such evidence had been found while he was alive, it might have put Hawking in line for the Nobel prize he had so desired, reports The Sunday Times.

“This was Stephen: to boldly go where Star Trek fears to tread,” said Hertog, professor of theoretical physics at KU Leuven University in Belgium.

“He has often been nominated for the Nobel and should have won it. Now he never can.”

REVEALED: Surprising things Stephen Hawking taught us

MORE: Stephen Hawking’s death shocks the world

The paper confronts an issue that had bothered Hawking since the 1983 “no-boundary” theory he devised with James Hartle.

In his “no boundary theory” devised with James Hartle, the pair described how the Earth hurtled into existence during the Big Bang.

But the theory also predicted a multiverse meaning the phenomenon was accompanied by a number of other “Big Bangs” creating separate universes.

In his final paper, Hawking, along with the professor for theoretical physics at KU Leuven University in Belgium, explored how these universes could be found using a probe on a spaceship.

The paper also predicted how our universe would eventually fade into blackness as the stars run out of energy.

Such ideas are controversial among cosmologists. Professor Neil Turok, director of Canada’s Perimeter Institute and a friend of Hawking’s, but who disagreed with his ideas, said: “I remain puzzled as to why he found this picture interesting.”

Other scientists said Hawking’s work might represent the breakthrough that cosmology needs, especially because it was the first such theory that could be tested in experiments.

The paper, called “A Smooth Exit from Eternal Inflation”, had its latest revisions approved on March 4, 10 days before Hawking’s passed away.

The Sunday Times reports that the paper is due to be published by an unnamed “leading journal” after a review is complete.

Hertog also told The Sunday Times he met with Hawking in person to get final approval before submitting the paper.

WHY HAWKING DIDN’T WIN A NOBEL PRIZE

`Hawking won accolades from his peers for having one of the most brilliant minds in science, but he never got a Nobel prize because no one has yet proven his ideas.

The Nobel committee looks for proof, not big ideas. Hawking was a deep thinker — a theorist — and his musings about black holes and cosmology have yet to get the lockdown evidence that accompanies the physics prizes, his fellow scientists said.

“The Nobel prize is not given to the smartest person or even the one who makes the greatest contribution to science. It’s given to discovery,” said California Institute of Technology physicist Sean Carroll.

“Hawking’s best theories have not yet been tested experimentally, which is why he hasn’t won a prize.” Hawking has often been compared to Nobel laureate Albert Einstein, and he died on the 139th anniversary of Einstein’s birth. But Einstein’s Nobel wasn’t for his famed theory of general relativity. It was for describing the photoelectric effect, and only after it was verified by Robert Millikan, said Harvard astronomer Avi Loeb.

HOW HAWKING’S VOICE DEVELOPED

Hawking’s computer-generated voice was known to millions of people around the world, a robotic drawl that somehow enhanced the profound impact of the cosmological secrets he revealed.

The technology behind his means of communication was upgraded through the years, offering him the chance to sound less like a machine, but he insisted on sticking to the original voice because it had effectively become his own. The renowned theoretical physicist, who died last week aged 76, lost his ability to speak more than three decades ago after a tracheotomy linked to complications in the motor neurone disease he was diagnosed with at the age of 21.

He later told the BBC he had considered committing suicide by not breathing after the operation, but he said the “reflex to breathe was too strong”. Hawking started to communicate again using his eyebrows to indicate letters on a spelling card.

A Cambridge University colleague contacted a company which had developed a program to allow a user to select words using a hand clicker, according to a 2014 report in Wired magazine.

It was linked to an early speech synthesiser, which turned Hawking’s text into spoken language.

In 1997, PC chipmaker Intel Corp stepped in to improve Hawking’s computer-based communication system, and in 2014 it upgraded the technology to make it faster and easier for Hawking to communicate.

It used algorithms developed by SwiftKey, a British software company best known for its predictive text technology used in smartphones.

Hawking provided lectures and other texts to help the algorithm learn his language, and it could predict the word he wanted to use by just inputting 10-15 per cent of the letters.

But despite the upgrades to the software, one thing remained constant: the voice itself.

Hawking stuck with the sound produced by his first speech synthesiser made in 1986.

It helped cement his place in popular culture.

“I keep it because I have not heard a voice I like better and because I have identified with it,” he said in 2006.

Part of this report was originally published by The Sun and has been republished with permission.

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Professor Stephen Hawking’s final theory on the origin of the universe, which he worked on in collaboration with Professor Thomas Hertog from KU Leuven, has been published in the Journal of High Energy Physics . 

We are not down to a single, unique universe, but our findings imply a significant reduction of the multiverse, to a much smaller range of possible universes. Stephen Hawking

The theory, which was submitted for publication before Hawking’s death earlier this year, is based on string theory and predicts the universe is finite and far simpler than many current theories about the big bang say.

Professor Hertog, whose work has been supported by the European Research Council, first announced the new theory at a conference at the University of Cambridge in July of last year, organised on the occasion of Professor Hawking’s 75 th birthday.

Modern theories of the big bang predict that our local universe came into existence with a brief burst of inflation – in other words, a tiny fraction of a second after the big bang itself, the universe expanded at an exponential rate. It is widely believed, however, that once inflation starts, there are regions where it never stops. It is thought that quantum effects can keep inflation going forever in some regions of the universe so that globally, inflation is eternal. The observable part of our universe would then be just a hospitable pocket universe, a region in which inflation has ended and stars and galaxies formed.

“The usual theory of eternal inflation predicts that globally our universe is like an infinite fractal, with a mosaic of different pocket universes, separated by an inflating ocean,” said Hawking in an interview last autumn. “The local laws of physics and chemistry can differ from one pocket universe to another, which together would form a multiverse. But I have never been a fan of the multiverse. If the scale of different universes in the multiverse is large or infinite the theory can’t be tested. ”

In their new paper, Hawking and Hertog say this account of eternal inflation as a theory of the big bang is wrong. “The problem with the usual account of eternal inflation is that it assumes an existing background universe that evolves according to Einstein’s theory of general relativity and treats the quantum effects as small fluctuations around this,” said Hertog. “However, the dynamics of eternal inflation wipes out the separation between classical and quantum physics. As a consequence, Einstein’s theory breaks down in eternal inflation.”

“We predict that our universe, on the largest scales, is reasonably smooth and globally finite. So it is not a fractal structure,” said Hawking.

The theory of eternal inflation that Hawking and Hertog put forward is based on string theory: a branch of theoretical physics that attempts to reconcile gravity and general relativity with quantum physics, in part by describing the fundamental constituents of the universe as tiny vibrating strings. Their approach uses the string theory concept of holography, which postulates that the universe is a large and complex hologram: physical reality in certain 3D spaces can be mathematically reduced to 2D projections on a surface.

Hawking and Hertog developed a variation of this concept of holography to project out the time dimension in eternal inflation. This enabled them to describe eternal inflation without having to rely on Einstein’ theory. In the new theory, eternal inflation is reduced to a timeless state defined on a spatial surface at the beginning of time.

“When we trace the evolution of our universe backwards in time, at some point we arrive at the threshold of eternal inflation, where our familiar notion of time ceases to have any meaning,” said Hertog.

Hawking’s earlier ‘no boundary theory’ predicted that if you go back in time to the beginning of the universe, the universe shrinks and closes off like a sphere, but this new theory represents a step away from the earlier work. “Now we’re saying that there is a boundary in our past,” said Hertog.

Hertog and Hawking used their new theory to derive more reliable predictions about the global structure of the universe. They predicted the universe that emerges from eternal inflation on the past boundary is finite and far simpler than the infinite fractal structure predicted by the old theory of eternal inflation.

Their results, if confirmed by further work, would have far-reaching implications for the multiverse paradigm. “We are not down to a single, unique universe, but our findings imply a significant reduction of the multiverse, to a much smaller range of possible universes,” said Hawking.

This makes the theory more predictive and testable.

Hertog now plans to study the implications of the new theory on smaller scales that are within reach of our space telescopes. He believes that primordial gravitational waves – ripples in spacetime – generated at the exit from eternal inflation constitute the most promising “smoking gun” to test the model. The expansion of our universe since the beginning means such gravitational waves would have very long wavelengths, outside the range of the current LIGO detectors. But they might be heard by the planned European space-based gravitational wave observatory, LISA, or seen in future experiments measuring the cosmic microwave background.

Reference: S.W. Hawking and Thomas Hertog. ‘ A Smooth Exit from Eternal Inflation? ’’ Journal of High-Energy Physics (2018). DOI: 10.1007/JHEP04(2018)147

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What Stephen Hawking’s Final Paper Says (And Doesn’t Say)

Before he died, renowned cosmologist Stephen Hawking submitted a paper, with co-author Thomas Hertog, to an as-yet-unknown journal. Hawking’s last known scientific writing, the paper deals with the concept of the multiverse and a theory known as cosmic inflation. Though the paper currently exists only in pre-print form , meaning it hasn’t completed the process of peer-review, it’s received a significant amount of coverage. “Stephen Hawking’s last paper,” after all, does have a bit of a mythological ring to it.

Stephen Hawking wrote a lot of papers, though. Most dealt with the same sort of heady concepts as his last, and few received such an inordinate amount of attention. Claims that the paper make predictions for the end of universe, or could prove the multiverse exists abound. But it’s worth remembering that the things Hawking thought and wrote about are abstract, they exist largely in the realm of theory. Even more well-known concepts like Hawking radiation have continued to elude scientists, so drawing solid conclusions from any one paper is difficult. Like many topics in theoretical physics, the ideas that Stephen Hawking pondered were so radical and far-out that we usually couldn’t even test them.

And even for one of the brightest minds of our time, the calculations are extremely complex. Hawking and Hertog describe their preliminary theory as a “toy model,” or one that significantly simplifies the real world to make the calculations easier. Such a model wouldn’t necessarily reflect the universe as we see it. No one said theoretical physics was easy.

Many Universes Stephen Hawking’s last paper is titled “A Smooth Exit from Eternal Inflation?” It tackles the idea of a multiverse, a vast collection of universes that exist simultaneously, though they’re spread out almost unimaginably far from each other. Multiverses arose, the theory goes, because of something called inflation. In the fractions of a second after our universe emerged, space-time expanded at an immense rate. As it did so, tiny quantum fluctuations expanded to become the large-scale features of the universe we observe today, and which serve as evidence that the theory might be true.

Under a variation of the theory that Hawking and Hertog work with, called eternal inflation, this inflation continues forever in most places, but, in some patches, it stops. Where it stops, universes form — our own and others, in a repeating process that never ends. In these universes, the laws of physics all look different, meaning constants we take for granted like the speed of light would vary between them.

“Eternal inflation creates an infinite number of patch universes, little bubble universes, all over the place with this inflating space between them,” says Will Kinney, a professor of physics at University at Buffalo College of Arts and Sciences.

But an infinite number of universes presents a problem to physicists. One of the most fundamental questions in science is why our universe looks the way it does. Why is the speed of light 186,282 miles per second? Determining the probability of our universe looking the way it does would help scientists get at the answer. Finding probabilities involving infinity is a useless exercise, though. What Hawking and Hertog have done, using a lot of complicated math, is to propose a way that we could define some boundaries on the kinds of universes that might exist.

“It’s like you have a bath full of lots and lots and lots of different kinds of soap bubbles and each soap bubble is a different universe, and there’s a huge variety of different soap bubbles of different shapes,” says Clifford Johnson, a professor in the Physics and Astronomy Department at the University of Southern California. “And what this model is suggesting is a mechanism by which maybe the variety of soap bubbles that are available is not as large as was thought.”

In addition, these universes might look a little more like ours, according to Katie Mack, an assistant professor of physics at North Carolina State University.

“The prediction is for … a smaller number of universes and they would have more in common with each other,” she says. “You could draw more of a straight line between the early universe and what we see today.”

Bringing Clarity If the kinds of universe that could possibly exist is finite, then scientists could begin to understand how and why our universe looks how it does today. Hawking’s paper does not tell us exactly what kind of universes might exist, nor does he definitively prove multiverse or cosmic inflation theories. As Kinney points out, Hawking and Hertog don’t even suggest any ways that we might be able to see evidence of the multiverse, meaning that their theory remains, for the moment, untestable.

The two rely on something called the holographic principle to conduct their work. It’s a way of reconciling quantum mechanics with gravity — the physics of the very large and the very small, as Mack, puts it. The holographic principle states that all of the information in a volume of space is contained in the boundary of the volume. In effect, it compresses a 3-D space into a 2-D space, and the end result is to make the calculations easier.

It’s something that many other researchers use in their work, and Johnson stresses that Hawking and Hertog’s paper, while intriguing, is simply another entry in the field.

“It’s two very good researchers adding a paper to the many very good papers that have been incrementally moving this framework of ideas,” Johnson says.

Hawking himself appears to have been still at work on the theory. Just weeks before his death, he submitted a newer version of the paper containing substantial changes. His co-author Hertog will surely continue to refine the work as well.

In the end, this paper is an interesting hypothesis about how our universe could look on the largest scale. It may not reshape our view of the cosmos — at least not yet — but it adds more intellectual firepower to our collective arsenal. And that’s probably what Stephen Hawking would have wanted.

This article originally appeared on Discovermagazine.com .

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Publications

Decade#toggle"> 2010's, a smooth exit from eternal inflation..

S.W. Hawking, T. Hertog. 24 Jul 2017. 14pp, arXiv:1707.07702 [hep-th]

The Conformal BMS Group.

S.J. Haco, S.W.Hawking, M.J.Perry, J.L.Bourjaily. 27 Jan 2017. 16pp, arXiv:1701.08110 [hep-th]

Superrotation Charge and Supertranslation Hair on Black Holes.

S.W. Hawking, M.J. Perry, A. Strominger. High Energ. Phys. (2017) 2017: 161. DOI: 10.1007/JHEP05(2017)161 .

Black holes: The Reith Lectures.

S.W. Hawking, May 2016, ISBN-13: 978-0857503572

George and the Blue Moon.

L. Hawking, S.W.Hawking, Mar 2016, ISBN-13: 978-0857533272

Soft Hair on Black Holes.,

S.W. Hawking, M.J. Perry, A. Strominger. Jan 5, 2016. 9pp. Published in Phys.Rev.Lett. 116 (2016) no.23, 231301, arXiv:1601.00921 DOI: 10.1103/PhysRevLett.116.231301

The Information Paradox for Black Holes

, S.W. Hawking. Sep 3, 2015. 3 pp. DAMTP-2015-49 e-Print: arXiv:1509.01147 [hep-th]

George and the Unbreakable Code.

L. Hawking. S.W.Hawking. Jun 2014. ISBN-13: 978-0857533258

Information Preservation and Weather Forecasting for Black Holes.

S.W. Hawking. Jan 2014. arXiv:1401.5761v1 [hep-th]

My Brief History.

S.W. Hawking, Sep 2013. 144 pp ISBN-13: 978-0345535283

Vector Fields in Holographic Cosmology.

James B.Hartle. S.W. Hawking, Thomas Hertog. May 2013. 17 pp. arXiv:1305.7190v1 [hep-th], DOI: 10.1007/JHEP11(2013)201

George and the Big Bang.

L. Hawking. S.W.Hawking. Aug 2012. ISBN-13: 978-1442440050

Quantum Probabilities for Inflation from Holography.

James B.Hartle. S.W. Hawking, Thomas Hertog. Jul 2012. arXiv:1207.6653v3 [hep-th], DOI: 10.1088/1475-7516/2014/01/015

Accelerated Expansion from Negative Lambda.

James B. Hartle (UC, Santa Barbara), S.W. Hawking (Cambridge U., DAMTP), Thomas Hertog (Leuven U. & Intl. Solvay Inst., Brussels). May 2012. 28 pp. arXiv:1205.3807v3 [hep-th]

George's Cosmic Treasure Hunt.

L. Hawking. S.W.Hawking. May 2011. ISBN-13: 978-1442421752

The dreams that stuff is made of: The most astounding papers of quantum physics - and how they shook the scientific world.

Stephen Hawking, (ed.) (Cambridge U., DAMTP). 2011. 1071 pp. Published in Philadelphia, USA: Running Pr. (2011) 1071 p. ISBN-13: 978-0762434343

Local Observation in Eternal inflation.

James Hartle (UC, Santa Barbara), S.W. Hawking (Cambridge U.,DAMTP), Thomas Hertog (APC, Paris & Intl. Solvay Inst., Brussels). Sep 2010. 4 pp. Published in Phys.Rev.Lett. 106 (2011) 141302. arXiv:1009.2525v2 [hep-th], DOI: 10.1103/PhysRevLett.106.141302

The Grand Design.

S.W.Hawking and L. Mlodinov (Sep 2010), ISBN-13: 978-0553805376

The No-Boundary Measure in the Regime of Eternal Inflation.

James Hartle (UC, Santa Barbara), S.W. Hawking (Cambridge U., DAMTP), Thomas Hertog (APC, Paris & Intl. Solvay Inst., Brussels). Jan 2010. 29 pp.Published in Phys.Rev. D82 (2010) 063510. arXiv:1001.0262v1 [hep-th], DOI: 10.1103/PhysRevD.82.063510

decade#toggle"> 2000's

George's secret key to the universe..

L. Hawking. S.W.Hawking. May 2009. ISBN-13: 978-1416985846

Why did the Universe Inflate?

S.W. Hawking (Cambridge U., DAMTP). 2009. 7 pp. DOI: 10.1007/978-0-387-87499-9_10

The Classical Universes of the No-Boundary Quantum State.

James B. Hartle (UC, Santa Barbara), S.W. Hawking (Cambridge U.,DAMTP), Thomas Hertog (APC, Paris & Intl. Solvay Inst., Brussels). Mar 2008. 46 pp. arXiv:0803.1663 [hep-th], DOI: 10.1103/PhysRevD.77.123537

No-Boundary Measure of the Universe.

James B. Hartle (UC, Santa Barbara), S.W. Hawking (Cambridge U., DAMTP), Thomas Hertog (APC, Paris & Intl. Solvay Inst., Brussels). Nov 2007. 4 pp. Published in Phys.Rev.Lett. 100 (2008) 201301. arXiv:0711.4630 [hep-th], DOI: 10.1103/PhysRevLett.100.201301

Volume Weighting in the No Boundary Proposal.

S.W. Hawking. Oct 2007. 7 pp. arXiv:0710.2029 [hep-th]

God created the Integers.

S.W.Hawking. Oct 2007. ISBN-13: 978-0762430048

The measure of the universe.

S.W. Hawking (Cambridge U., DAMTP). 2007. 6 pp. Published in AIP Conf.Proc. 957 (2007) 79-84, DOI: 10.1063/1.2823830

Populating the landscape: A Top down approach

. S.W. Hawking (Cambridge U., DAMTP), Thomas Hertog (CERN). CERN-PH-TH-2006-022. Feb 2006. 22 pp. Published in Phys.Rev. D73 (2006) 123527. arXiv:hep-th/0602091 , DOI: 10.1103/PhysRevD.73.123527

Information loss in black holes.

S.W. Hawking (Cambridge U., DAMTP). DAMTP-2005-66. Jul 2005. 5 pp.Published in Phys.Rev. D72 (2005) 084013. arXiv:hep-th/0507171 , DOI: 10.1103/PhysRevD.72.084013

A non singular universe.

S. Hawking (Cambridge U., DAMTP). 2005. 2 pp. Published in Phys.Scripta T117 (2005) 49-50

A briefer history of time.

S. Hawking (Cambridge U., DAMTP), L. Mlodinow. 2005. 189 pp. Published in Reinbek, Germany: Rowohlt (2005) 189 p. ISBN-13: 978-0553385465

Black holes and the information paradox.

S. Hawking (Cambridge U., DAMTP). Jul 2004. 7 pp. Prepared for Conference: C04-07-18 , p.56-62 Proceedings

The grand Stephen Hawking reader: Life and work.

H. Mania, (ed.), S. Hawking. 2004. 291 pp. Published in (rororo. 61655)

On the Shoulders of Giants.

N. Copernicus, J. Kepler, G. Galalei, I. Newton, A. Einstein (Author), S. Hawking. Dec 2003. ISBN-13: 978-0762416981

Cosmology from the top down.

Stephen W. Hawking (Cambridge U., DAMTP). DAVISINFLATION-2003-PELLY. May 2003. Published in In *Carr, Bernard (ed.): Universe or multiverse?* 91-98. arXiv:astro-ph/0305562

The illustrated theory of everything: The origin and fate of the universe.

S.W. Hawking (Cambridge U., DAMTP). 2003. 119 pp. Published in Beverly Hills, USA: New Millennium Pr. (2003) 119 p

Brane new world.

Stephen Hawking (Cambridge U., DAMTP). Aug 2002. 7 pp. Published in Conf.Proc. C0208124 (2002) 1-7

Why does inflation start at the top of the hill?

S.W Hawking, Thomas Hertog (Cambridge U., DAMTP). Apr 2002. 21 pp. Published in Phys.Rev. D66 (2002) 123509. arXiv:hep-th/0204212 , DOI: 10.1103/PhysRevD.66.123509

Sixty years in a nutshell.

S. Hawking (Newton Inst. Math. Sci., Cambridge). Jan 2002. Prepared for Workshop on Conference on the Future of Conference: C02-01-07.7

Chronology protection: Making the world safe for historians.

S.W. Hawking. 2002. Published in In *Hawking, S.W. et al.: The future of spacetime* 87-108

The Future of space-time.

S.W. Hawking, K.S. Thorne, I. Novikov, T. Ferris, A. Lightman, R. Price. 2002. 220 pp.Published in New York, USA: Norton (2002) 220 p

S.W. Hawking (Cambridge U., DAMTP). Nov 2001. Prepared for Conference: C01-11-13.1

Living with ghosts.

S.W. Hawking, Thomas Hertog (Cambridge U., DAMTP). Jul 2001. 13 pp. Published in Phys.Rev. D65 (2002) 103515. arXiv:hep-th/0107088 , DOI: 10.1103/PhysRevD.65.103515

The universe in a nutshell.

S. Hawking (Cambridge U., DAMTP). 2001. 224 pp. ISBN-13: 978-0553802023

Trace anomaly driven inflation.

S.W. Hawking, T. Hertog (Cambridge U., DAMTP), H.S. Reall (Queen Mary, U. of London). DAMTP-2000-92, QMW-PH-00-10. Oct 2000. 40 pp. Published in Phys.Rev. D63 (2001) 083504. arXiv:hep-th/0010232 , DOI: 10.1103/PhysRevD.63.083504

Large N cosmology.

S.W. Hawking (Cambridge U., DAMTP). Sep 2000. Prepared for Conference: C00-09-04.4

S.W. Hawking, T. Hertog, H.S. Reall (Cambridge U., DAMTP). DAMTP-2000-25. Mar 2000. 28 pp.Published in Phys.Rev. D62 (2000) 043501. arXiv:hep-th/0003052 , DOI: 10.1103/PhysRevD.62.043501

Gravitational waves in open de Sitter space.

S.W. Hawking, Thomas Hertog, Neil Turok (Cambridge U., DAMTP). Mar 2000. 17 pp. Published in Phys.Rev. D62 (2000) 063502. arXiv:hep-th/0003016 , DOI: 10.1103/PhysRevD.62.063502

de Sitter entropy, quantum entanglement and AdS / CFT.

Stephen Hawking (Cambridge U., DAMTP), Juan Martin Maldacena, Andrew Strominger (Harvard U.). Feb 2000. 14 pp. Published in JHEP 0105 (2001) 001. arXiv:hep-th/0002145 , DOI: 10.1088/1126-6708/2001/05/001

Stability of AdS and phase transitions.

S.W. Hawking (Cambridge U., DAMTP). 2000. Published in Class.Quant.Grav. 17 (2000) 1093-1099, DOI: 10.1088/0264-9381/17/5/318

decade#toggle"> 1990's

Rane world black holes..

B A. Chamblin, S.W. Hawking, H.S. Reall (Cambridge U., DAMTP). DAMTP-1999-133. Sep 1999. 9 pp. Published in Phys.Rev. D61 (2000) 065007. arXiv:hep-th/9909205 , DOI: 10.1103/PhysRevD.61.065007

Charged and rotating AdS black holes and their CFT duals.

S.W. Hawking, H.S. Reall (Cambridge U., DAMTP). DAMTP-R-99-108. Aug 1999. 18 pp. Published in Phys.Rev. D61 (2000) 024014. arXiv:hep-th/9908109 , DOI: 10.1103/PhysRevD.61.024014

Primordial black holes: Pair creation, Lorentzian condition, and evaporation.

R. Bousso (Stanford U., Phys. Dept.), S.W. Hawking (Cambridge U.). 1999. Published in Int.J.Theor.Phys. 38 (1999) 1227-, DOI: 10.1023/A:1026618832525

A debate on open inflation.

S.W. Hawking (Cambridge U., DAMTP). Nov 1998. Published in AIP Conf.Proc. 478 (1999) 15-22

Rotation and the AdS / CFT correspondence.

S.W. Hawking, C.J. Hunter, Marika Taylor (Cambridge U., DAMTP). Nov 1998. 24 pp. Published in Phys.Rev. D59 (1999) 064005. arXiv:hep-th/9811056 , DOI: 10.1103/PhysRevD.59.064005

Nut charge, anti-de Sitter space and entropy.

S.W. Hawking, C.J. Hunter (Cambridge U.), Don N. Page (Alberta U.). DAMTP-98-122. Sep 1998. 13 pp. Published in Phys.Rev. D59 (1999) 044033. arXiv:hep-th/9809035 , DOI: 10.1103/PhysRevD.59.044033

Gravitational entropy and global structure.

S.W. Hawking, C.J. Hunter (Cambridge U.). DAMTP-98-104. Aug 1998. 19 pp. Published in Phys.Rev. D59 (1999) 044025. arXiv:hep-th/9808085 , DOI: 10.1103/PhysRevD.59.044025

Open inflation.

S.W. Hawking (CAMBRIDGE U.). Aug 1998. Prepared for 2nd Samos Meeting on Cosmology, Geometry and Re Conference: C98-08-31.4

Lorentzian condition in quantum gravity.

Raphael Bousso (Stanford U., Phys. Dept.), Stephen W. Hawking (Cambridge U.). SU-ITP-98-26, DAMTP-98-87. Jul 1998. 14 pp. Published in Phys.Rev. D59 (1999) 103501, Erratum-ibid. D60 (1999) 109903. arXiv:hep-th/9807148 , DOI: 10.1103/PhysRevD.60.109903 , 10.1103/PhysRevD.59.103501

Inflation, singular instantons and eleven-dimensional cosmology.

S.W. Hawking, Harvey S. Reall (Cambridge U.). DAMTP-98-85. Jul 1998. 19 pp. Published in Phys.Rev. D59 (1999) 023502. arXiv:hep-th/9807100 , DOI: 10.1103/PhysRevD.59.023502

Open inflation, the four form and the cosmological constant.

Neil Turok, S.W. Hawking (Cambridge U.). Mar 1998. 11 pp. Published in Phys.Lett. B432 (1998) 271-278. arXiv:hep-th/9803156 , DOI: 10.1016/S0370-2693(98)00651-0

Open inflation without false vacua.

S.W. Hawking, Neil Turok (Cambridge U.). Feb 1998. 10 pp. Published in Phys.Lett. B425 (1998) 25-32. arXiv:hep-th/9802030 , DOI: 10.1016/S0370-2693(98)00234-2

Comment on 'quantum creation of an open universe', by Andrei Linde.

S.W. Hawking, Neil Turok (Cambridge U.). Feb 1998. 4 pp. arXiv:gr-qc/9802062

Is information lost in black holes?.

S.W. Hawking (Cambridge U.). 1998. Published in In *Wald, R.M. (ed.): Black holes and relativistic stars* 221-240

Bulk charges in eleven-dimensions.

S.W. Hawking, Marika Taylor (Cambridge U.). DAMTP-R-97-52. Nov 1997. 26 pp. Published in Phys.Rev. D58 (1998) 025006. arXiv:hep-th/9711042 , DOI: 10.1103/PhysRevD.58.025006

Evaporation of cosmological black holes.

R. Bousso (Stanford U., Phys. Dept.), S.W. Hawking (Cambridge U., DAMTP). Nov 1997. 14 pp. Prepared for Conference: C97-11-11.1

(Anti)evaporation of Schwarzschild-de Sitter black holes.

Raphael Bousso, Stephen W. Hawking (Cambridge U.). DAMTP-R-97-26. Sep 1997. 16 pp. Published in Phys.Rev. D57 (1998) 2436-2442. arXiv:hep-th/9709224 , DOI: 10.1103/PhysRevD.57.2436

Models for chronology selection.

M.J. Cassidy, S.W. Hawking (Cambridge U.). DAMTP-R-97-47. Sep 1997. 20 pp.Published in Phys.Rev. D57 (1998) 2372-2380. arXiv:hep-th/9709066 , DOI: 10.1103/PhysRevD.57.2372

Evaporation of primordial black holes.

S.W. Hawking (Cambridge U., DAMTP). Aug 1997. Prepared for 6th Conference on Quantum Mechanics of Conference: C97-11-11.1

Trace anomaly of dilaton coupled scalars in two-dimensions.

Raphael Bousso, Stephen W. Hawking (Cambridge U.). DAMTP-R-97-25. May 1997. 11 pp. Published in Phys.Rev. D56 (1997) 7788-7791. arXiv:hep-th/9705236 , DOI: 10.1103/PhysRevD.56.7788

Loss of quantum coherence through scattering off virtual black holes.

S.W. Hawking (Cambridge U.), Simon F. Ross (UC, Santa Barbara). DAMTP-R-97-21, UCSB-TH-97-08. May 1997. 29 pp. Published in Phys.Rev. D56 (1997) 6403-6415. arXiv:hep-th/9705147 , DOI: 10.1103/PhysRevD.56.6403

Evolution of near extremal black holes.

S.W. Hawking, Marika Taylor (Cambridge U.). DAMTP-R-96-56. Feb 1997. 25 pp. Published in Phys.Rev. D55 (1997) 7680-7692. arXiv:hep-th/9702045 , DOI: 10.1103/PhysRevD.55.7680

R. Bousso (Stanford U., Phys. Dept.), S.W. Hawking (Cambridge U., DAMTP). 1997. Published in In *Ambleside 1997, Particle physics and the early universe* 481-494

The Nature of space and time.

S.W. Hawking, R. Penrose. Jul 1996. Published in Sci.Am. 275 (1996) 44-49

Pair creation of black holes during inflation.

Raphael Bousso, Stephen W. Hawking (Cambridge U.). DAMTP-R-96-33. Jun 1996. 29 pp. Published in Phys.Rev. D54 (1996) 6312-6322

Loss of information in black holes.

S. Hawking (Cambridge U., DAMTP). Jun 1996. Prepared for Conference on Geometric Issues in Foundations Conference: C96-06-25.2

Primordial black holes: Tunneling versus no boundary proposal.

Raphael Bousso, Stephen W. Hawking (Cambridge U., DAMTP). DAMTP-R-96-34, C96-05-25. May 1996. 14 pp. Published in Grav.Cosmol.Suppl. 4 (1998) 28-37. arXiv:gr-qc/9608009

Pair creation and evolution of black holes in inflation.

Raphael Bousso, Stephen W. Hawking (Cambridge U.). DAMTP-R-96-35, C96-05-26. May 1996. 8 pp. Published in Helv.Phys.Acta 69 (1996) 261-264. arXiv:gr-qc/9608008 , DOI: 10.1103/PhysRevD.54.6312

The Gravitational Hamiltonian in the presence of nonorthogonal boundaries.

S.W. Hawking, C.J. Hunter (Cambridge U.). DAMTP-R-96-9. Mar 1996. 19 pp. Published in Class.Quant.Grav. 13 (1996) 2735-2752. arXiv:gr-qc/9603050 , DOI: 10.1088/0264-9381/13/10/012

Black holes in inflation.

R. Bousso, S.W. Hawking (Cambridge U., DAMTP). 1996. Published in Nucl.Phys.Proc.Suppl. 57 (1997) 201-205, DOI: 10.1016/S0920-5632(97)00377-0

S. Hawking, R. Penrose. 1996. Published in Princeton, USA: Univ. Pr. (1996) 141 p. (The Isaac Newton Institute series of lectures)

Virtual black holes.

S.W. Hawking (Cambridge U.). DAMTP-R-95-50. Oct 1995. 24 pp. Published in Phys.Rev. D53 (1996) 3099-3107. arXiv:hep-th/9510029 , DOI: 10.1103/PhysRevD.53.3099

Black holes and baby universes and other essays.

S. Hawking. 1995. Published in Toronto, Canada: Bantam Books (1994) 172 p, ISBN-13: 978-0553374117

The Probability for primordial black holes.

R. Bousso, S.W. Hawking (Cambridge U.). DAMTP-R-95-33. Jun 1995. 15 pp. Published in Phys.Rev. D52 (1995) 5659-5664. arXiv:gr-qc/9506047 , DOI: 10.1103/PhysRevD.52.5659

Pair production of black holes on cosmic strings.

S.W. Hawking, Simon F. Ross (Cambridge U.). DAMTP-R-95-30. Jun 1995. 9 pp. Published in Phys.Rev.Lett. 75 (1995) 3382-3385. arXiv:gr-qc/9506020 , DOI: 10.1103/PhysRevLett.75.3382

Duality between electric and magnetic black holes.

S.W. Hawking, Simon F. Ross (Cambridge U.). DAMTP-R-95-8. Apr 1995. 16 pp. Published in Phys.Rev. D52 (1995) 5865-5876. arXiv:hep-th/9504019 , DOI: 10.1103/PhysRevD.52.5865

The Gravitational Hamiltonian, action, entropy and surface terms.

S.W. Hawking (Cambridge U.), Gary T. Horowitz (UC, Santa Barbara). DAMTP-R-94-52, UCSBTH-94-37. Jan 1995. 13 pp. Published in Class.Quant.Grav. 13 (1996) 1487-1498. arXiv:gr-qc/9501014 , DOI: 10.1088/0264-9381/13/6/017

Quantum coherence and closed timelike curves.

S.W. Hawking (Cambridge U.). DAMTP-R-95-04. Jan 1995. 12 pp. Published in Phys.Rev. D52 (1995) 5681-5686. arXiv:gr-qc/9502017 , DOI: 10.1103/PhysRevD.52.5681

Entropy, Area, and black hole pairs.

S.W. Hawking, Gary T. Horowitz (Newton Inst. Math. Sci., Cambridge), Simon F. Ross (Cambridge U.). NI-94-012, DAMTP-R-94-26, UCSBTH-94-25. Sep 1994. 24 pp. Published in Phys.Rev. D51 (1995) 4302-4314. arXiv:gr-qc/9409013 , DOI: 10.1103/PhysRevD.51.4302

Nature of space and time.

S.W. Hawking (Cambridge U.). Sep 1994. 62 pp. arXiv:hep-th/9409195

Euclidean quantum gravity.

G.W. Gibbons, (ed.), S.W. Hawking, (ed.) (Cambridge U.). 1994. Published in Singapore, Singapore: World Scientific (1993) 586 p

The Superscattering matrix for two-dimensional black holes.

S.W. Hawking (Cambridge U. & Caltech). Nov 1993. 12 pp. Published in Phys.Rev. D50 (1994) 3982-3986. arXiv:hep-th/9401109 , DOI: 10.1103/PhysRevD.50.3982

Quantum coherence in two-dimensions.

S.W. Hawking, J.D. Hayward (Cambridge U. & Caltech). CALT-68-1861, DAMTP-R-93-12. Mar 1993. 14 pp. Published in Phys.Rev. D49 (1994) 5252-5256. arXiv:hep-th/9305165 , DOI: 10.1103/PhysRevD.49.5252

Supersymmetric Bianchi models and the square root of the Wheeler-DeWitt equation.

P.D. D'Eath, S.W. Hawking (Cambridge U.), O. Obregon (Guanajuato U., FIMEE). DAMTP-R-92-44. Feb 23, 1993. 11 pp. Published in Phys.Lett. B300 (1993) 44-48, DOI: 10.1016/0370-2693(93)90746-5

The Origin of time asymmetry.

S.W. Hawking (Cambridge U.), R. Laflamme (Cambridge U. & Los Alamos), G.W. Lyons (Cambridge U.). PRINT-93-0178 (DAMTP,CAMBRIDGE). Feb 12, 1993. 41 pp. Published in Phys.Rev. D47 (1993) 5342-5356. arXiv:gr-qc/9301017 , DOI: 10.1103/PhysRevD.47.5342

Einstein's dream: Expeditions to the frontiers of space-time. Black holes and baby universes and other essays. (In German).

S.W. Hawking. 1993. Published in Reinbek, Germany: Rowohlt (1993) 190 p

Naked and thunderbolt singularities in black hole evaporation.

S.W. Hawking, J.M. Stewart (Cambridge U.). PRINT-92-0362 (DAMTP,CAMBRIDGE), DAMTP-R-92-37. Jul 1992. 28 pp. Published in Nucl.Phys. B400 (1993) 393-415. arXiv:hep-th/9207105 , DOI: 10.1016/0550-3213(93)90410-Q

Evaporation of two-dimensional black holes.

S.W. Hawking (Caltech & Cambridge U.). CALT-68-1774. Mar 20, 1992. 11 pp. Published in Phys.Rev.Lett. 69 (1992) 406-409. arXiv:hep-th/9203052 , DOI: 10.1103/PhysRevLett.69.406

Kinks and topology change.

G.W. Gibbons, S.W. Hawking (Cambridge U.). 1992. Published in Phys.Rev.Lett. 69 (1992) 1719-1721, DOI: 10.1103/PhysRevLett.69.1719

S.W. Hawking (Cambridge U.). 1992. Published in In *Trieste 1992, Proceedings, The renaissance of general relativity and cosmology* 274-286

Selection rules for topology change.

G.W. Gibbons, S.W. Hawking (Cambridge U.). PRINT-91-0452 (DAMTP,CAMBRIDGE). Nov 12, 1991. 14 pp. Published in Commun.Math.Phys. 148 (1992) 345-352, DOI: 10.1007/BF02100864

The no boundary condition and the arrow of time.

S.W. Hawking (Cambridge U., DAMTP). Sep 1991. Prepared for NATO Workshop on the Physical Origin of Conference: C91-09-30.4

The Chronology protection conjecture.

S.W. Hawking (Cambridge U.). DAMTP-R-91-15. Jul 1991. 24 pp.Published in Phys.Rev. D46 (1992) 603-611, DOI: 10.1103/PhysRevD.46.603

Wormholes in string theory.

Alex Lyons (Alberta U.), S.W. Hawking (Cambridge U.). ALBERTA-THY-5-91. May 1991. 40 pp. Published in Phys.Rev. D44 (1991) 3802-3818, DOI: 10.1103/PhysRevD.44.3802

The Alpha parameters of wormholes.

S.W. Hawking (Cambridge U.). 1991. Published in Phys.Scripta T36 (1991) 222-227, DOI: 10.1088/0031-8949/1991/T36/023

The chronology protection conjecture.

S.W. Hawking (Cambridge U., DAMTP). 1991. Published in In *Kyoto 1991, Recent developments in theoretical and experimental general relativity, gravitation and relativistic field theories, pt. A* 3-13

Beginning or end? Inaugural lecture. (In German).

S. Hawking, (ed.) (Cambridge U.). 1991. Published in Paderborn, Germany: Junfermann (1991) 43 p

The Effective action for wormholes.

S.W. Hawking (Cambridge U.). PRINT-90-0682 (CAMBRIDGE). Nov 23, 1990. 19 pp. Published in Nucl.Phys. B363 (1991) 117-131, DOI: 10.1016/0550-3213(91)90237-R

The beginning of the universe.

S.W. Hawking (Cambridge U., DAMTP). Sep 1990. Prepared for (IUPAP) International Conference on Primordial Conference: C90-09-04.2

The spectrum of wormholes.

S.W. Hawking (Santa Barbara, KITP & Cambridge U.), Don N. Page (Santa Barbara, KITP & Penn State U. & Alberta U.). NSF-ITP-90-76. Jun 17, 1990. 37 pp. Published in Phys.Rev. D42 (1990) 2655-2663, DOI: 10.1103/PhysRevD.42.2655

Gravitational radiation from collapsing cosmic string loops.

S.W. Hawking (Cambridge U.). DAMTP/R-90-14. Apr 1990. 7 pp. Published in Phys.Lett. B246 (1990) 36-38, DOI: 10.1016/0370-2693(90)91304-T

Wormholes and nonsimply connected manifolds.

S.W. Hawking (Cambridge U.). DAMTP-R-90-13. Jan 1990. 23 pp. Published in In *Jerusalem 1989, Proceedings, Quantum cosmology and baby universes* 245-267 and Cambridge Univ. - DAMTP-R-90-13 (90,rec.Jul.) 23 p

Baby universes. 2.

S.W. Hawking (Cambridge U.). 1990. Published in Mod.Phys.Lett. A5 (1990) 453-466, DOI: 10.1142/S0217732390000524

Wormholes in dimensions 1 - 4.

S.W. Hawking (Cambridge U.). 1990. Published in In *Boston 1990, Proceedings, Particles, strings and cosmology* 623-634. (see HIGH ENERGY PHYSICS INDEX 29 (1991) No.9950)

The Formation and evolution of cosmic strings. Proceedings, Workshop, Cambridge, UK, July 3-7, 1989.

G.W. Gibbons, (ed.), S.W. Hawking, (ed.), T. Vachaspati, (ed.) (Cambridge U. & Tufts U.). 1990. Published in Cambridge, UK: Univ. Pr. (1990) 542 p

decade#toggle"> 1980's

Do wormholes fix the constants of nature.

S.W. Hawking (Cambridge U.). Print-89-0795 (CAMBRIDGE), DAMTP/R-89/13. May 1989. 12 pp. Published in Nucl.Phys. B335 (1990) 155, DOI: 10.1016/0550-3213(90)90175-D

The Edge Of Space-time.

S. Hawking (Cambridge U.). 1989. Published in IN *DAVIES, P. (ED.): THE NEW PHYSICS* 61-69

Baby Universes And The Nonrenormalizability Of Gravity.

S.W. Hawking, R. Laflamme (Cambridge U.). Print-88-0290(CAMBRIDGE), DAMTP/R-88/3. Mar 1988. 6 pp. Published in Phys.Lett. B209 (1988) 39, DOI: 10.1016/0370-2693(88)91825-4

Wormholes in Space-Time.

S.W. Hawking (Cambridge U.). 1988. Published in Phys.Rev. D37 (1988) 904-910, DOI: 10.1103/PhysRevD.37.904

Baby universes.

S.W. Hawking (Cambridge U.). 1988. Published in In *Leningrad 1988, Proceedings, A.A. Friedmann:Centenary volume* 81-92.

ABrief History Of Time.

S.W. Hawking. 1988. Published by Bantam (Sep 1988) 212p, ISBN-13: 978-0553380163

Quantum Cosmology.

S.W. Hawking (Cambridge U.). 1988. Published in IN *FANG, LI-ZHI (ED.), RUFFINI, R. (ED.): QUANTUM COSMOLOGY*, 190-235 AND PREPRINT - HAWKING, S.W. (83,REC.DEC.) 64 P.

The Quantum Theory Of The Universe.

S.W. Hawking (Cambridge U.). 1988. Published in IN *JERUSALEM 1983/84, PROCEEDINGS, INTERSECTION BETWEEN ELEMENTARY PARTICLE PHYSICS AND COSMOLOGY*, 71-97.

Black Holes From Cosmic Strings.

S.W. Hawking (Cambridge U.). Print-88-0310 (CAMBRIDGE). Dec 1987. 5 pp.Published in Phys.Lett. B231 (1989) 237, DOI: 10.1016/0370-2693(89)90206-2

The Direction Of Time.

S.W. Hawking (Cambridge U.). Print-87-0849 (DAMTP). Nov 10, 1987. 10 pp. Published in New Sci. 115 (1987) 46

How probable is inflation?.

S.W. Hawking (Cambridge U.), Don N. Page (Penn State U.). Print-87-0739 (PENN STATE). Jun 1987. 30 pp. Published in Nucl.Phys. B298 (1988) 789-809, DOI: 10.1016/0550-3213(88)90008-9

The Origin Of The Universe.

S.W. Hawking (Cambridge U.). Print-87-0841 (CAMBRIDGE). Jun 1987. 10 pp.

The Ground State Of The Universe.

S.W. Hawking (Cambridge U.). Print-87-0845 (CAMBRIDGE), C87/05/01.2. May 1987. 3 pp. Closing Remarks given at Conference: C87-05-01.2

Quantum Coherence Down the Wormhole.

S.W. Hawking (Cambridge U.). Print-87-0842 (CAMBRIDGE). Apr 1987. 12 pp. Published in Phys.Lett. B195 (1987) 337, DOI: 10.1016/0370-2693(87)90028-1

The Schrodinger Equation In Quantum Cosmology And String Theory.

S.W. Hawking (Cambridge U.). Print-87-0843 (CAMBRIDGE). Mar 1987. 10 pp.

Three Hundred Years Of Gravitation.

S.W. Hawking, (Ed.), W. Israel, (Ed.). 1987. Published in Cambridge, UK: Univ. Pr. (1987) 684 p

S.W. Hawking (Cambridge U.). Print-87-0166 (CAMBRIDGE), C87/06/29. Dec 1986. 31 pp.Published in In *Hawking, S.W. (ed.), Israel, W. (ed.): Three hundred years of gravitation*, 631-651 and Preprint - Hawking, S.W. (86,rec.Jan.87) 31 p

A Natural Measure On The Set Of All Universes.

G.W. Gibbons, S.W. Hawking, J.M. Stewart (Cambridge U.).PRINT-86-1241. Oct 14, 1986. 19 pp. Published in Nucl.Phys. B281 (1987) 736, DOI: 10.1016/0550-3213(87)90425-1

The Density Matrix Of The Universe.

S.W. Hawking (Cambridge U.). PRINT-86-0918 (CAMBRIDGE). Apr 1986. 10 pp. Published in Phys.Scripta T15 (1987) 151, DOI: 10.1088/0031-8949/1987/T15/020

Lectures On Quantum Cosmology.

S.W. Hawking (Cambridge U.). 1986. Published in In *Kyoto 1985, Proceedings, Quantum Gravity and Cosmology*, 170-206

Lectures On Quantum Cosmology

S.W. Hawking (Cambridge U.). 1986. Published in In *De Vega, H.j. ( Ed.), Sanchez, N. ( Ed.): Field Theory, Quantum Gravity and Strings*, 1-45

Who's Afraid Of (higher Derivative) Ghosts?.

S.W. Hawking (Cambridge U.). Print-86-0124 (CAMBRIDGE). Sep 1985. 16 pp. Published in IN *BATALIN, I.A. (ED.) ET AL.: QUANTUM FIELD THEORY AND QUANTUM STATISTICS, VOL. 2*, 129-139. link

Operator Ordering and the Flatness of the Universe.

S.W. Hawking (Cambridge U.), Don N. Page (Penn State U.). PRINT-85-0503 (PENN-STATE). Apr 1985. 21 pp. Published in Nucl.Phys. B264 (1986) 185-196, DOI: 10.1016/0550-3213(86)90478-5

The Arrow Of Time In Cosmology.

S.W. Hawking (Cambridge U.). Print-85-0492 (CAMBRIDGE). Apr 1985.23 pp.Published in Phys.Rev. D32 (1985) 2489, DOI: 10.1103/PhysRevD.32.2489

Quantum Cosmology - Beyond Minisuperspace.

J. Halliwell, S. Hawking (Cambridge U.). 1985. Published in In *Rome 1985, Proceedings, General Relativity, Pt. A*, 65-83

The Quantum Mechanics Of The Universe.

S.W. Hawking (Cambridge U.). 1985. Published in In *Geneva 1983, Proceedings, Large-scale Structure Of The Universe, Cosmology and Fundamental Physics*, 415-422

The Origin of Structure in the Universe.

J.J. Halliwell, S.W. Hawking (Cambridge U. & Munich, Max Planck Inst.). Print-85-0265 (CAMBRIDGE). Oct 1984. 48 pp. Published in Phys.Rev. D31 (1985) 1777, DOI: 10.1103/PhysRevD.31.1777

Limits On Inflationary Models Of The Universe.

S.W. Hawking (Cambridge U.). Print-85-0067 (CAMBRIDGE). Sep 1984. 8 pp. Published in Phys.Lett. B150 (1985) 339, DOI: 10.1016/0370-2693(85)90989-X

Higher Derivatives In Quantum Cosmology. 1. The Isotropic Case.

S.W. Hawking, J.C. Luttrell (Cambridge U.). Print-84-0711 (CAMBRIDGE). Aug 1984. 16 pp. Published in Nucl.Phys. B247 (1984) 250, DOI: 10.1016/0550-3213(84)90380-8

Nontrivial Topologies In Quantum Gravity.

S.W. Hawking (Cambridge U.). Print-84-0714 (CAMBRIDGE). Aug 1984. 16 pp. Published in Nucl.Phys. B244 (1984) 135, DOI: 10.1016/0550-3213(84)90185-8

NumericalCalculations Of Minisuperspace Cosmological Models.

S.W. Hawking, Z.C. Wu (Cambridge U.). Print-84-0913 (CAMBRIDGE). Jul 1984. 18 pp. Published in Phys.Lett. B151 (1985) 15, DOI: 10.1016/0370-2693(85)90815-9

The Isotropy Of The Universe.

Stephen W. Hawking, Julian C. Luttrell (Cambridge U.). Print-84-0479 (CAMBRIDGE). Jun 1984. 8 pp. Published in Phys.Lett. B143 (1984) 83, DOI: 10.1016/0370-2693(84)90809-8

The Cosmological Constant Is Probably Zero.

S.W. Hawking (Cambridge U.).Print-84-0116 (CAMBRIDGE). Feb 1984. 5 pp. Published in Phys.Lett. B134 (1984) 403, DOI: 10.1016/0370-2693(84)91370-4

Quantum Fluctuations As The Cause Of Inhomogeneity In The Universe.

J. Halliwell, S.W. Hawking (Cambridge U.). 1984. Published in In *Moscow 1984, Proceedings, Quantum Gravity*, 509-565

The Very Early Universe. Proceedings, Nuffield Workshop, Cambridge, Uk, June 21 - July 9, 1982.

G.W. Gibbons, (Ed.), S.W. Hawking, (Ed.), S.T.C. Siklos, (Ed.). 1984. Published in Cambridge, Uk: Univ. Pr. ( 1983) 480p

The Quantum State of the Universe.

S.W. Hawking (Cambridge U.). PRINT-84-0117 (CAMBRIDGE). Nov 1983. 28 pp. Published in Nucl.Phys. B239 (1984) 257, DOI: 10.1016/0550-3213(84)90093-2

The Unification Of Physics.

S.W. Hawking (Cambridge U.). Print-84-0115 (CAMBRIDGE). Aug 1983. 10 pp.

Wave Function of the Universe.

J.B. Hartle (Chicago U., EFI& Santa Barbara, KITP), S.W. Hawking (Cambridge U. & Santa Barbara, KITP). PRINT-83-0937 (CAMBRIDGE). Jul 983. 46 pp. Published in Phys.Rev. D28 (1983) 2960-2975, DOI: 10.1103/PhysRevD.28.2960

S.W. Hawking (Cambridge U.). PRINT-84-0114 (CAMBRIDGE), C83-06-27.1. Jul 1983. 64 pp.Published in In *Les Houches 1983, Proceedings, Relativity, Groups and Topology, Ii*, 333-379 and Preprint - HAWKING, S.W. (83,REC.DEC.) 64p

Euclidean Approach To The Inflationary Universe.

S.W. Hawking (Cambridge U.). Print-83-0318 (CAMBRIDGE). Apr 1983. 10 pp. Published in In *Cambridge 1982, Proceedings, The Very Early Universe*, 287-296 and Preprint -HAWKING, S.W. (REC.APR.83) 12p

The Boundary Conditions For Gauged Supergravity.

S.W. Hawking (Cambridge U.). Print-83-0317 (CAMBRIDGE). Mar 1983. 11 pp. Published in Phys.Lett. B126 (1983) 175, DOI: 10.1016/0370-2693(83)90585-3

Fluctuations In The Inflationary Universe

. S.W. Hawking (Cambridge U.), I.G. Moss (Newcastle upon Tyne U.). PRINT-83-0316 (CAMBRIDGE). Dec 1982. 20 pp. Published in Nucl.Phys. B224 (1983) 180, DOI: 10.1016/0550-3213(83)90319-X

Thermodynamics of Black Holes in anti-De Sitter Space.

S.W. Hawking (Cambridge U.), Don N. Page (Penn State U.). PRINT-83-0019 (CAMBRIDGE). Jul 1982. 18 pp.Published in Commun.Math.Phys. 87 (1983) 577, DOI: 10.1007/BF01208266

Positive Mass Theorems For Black Holes.

G.W. Gibbons, S.W. Hawking (Cambridge U.), Gary T. Horowitz (Princeton, Inst. Advanced Study), Malcolm J. Perry (Princeton U.). Print-82-0505 (PRINCETON). Jul 1982. 25 pp.Published in Commun.Math.Phys. 88 (1983) 295, DOI: 10.1007/BF01213209

The Development of Irregularities in a Single Bubble Inflationary Universe.

S.W. Hawking (Cambridge U.). Print-83-0015 (CAMBRIDGE). Jun 1982. 8 pp. Published in Phys.Lett. B115 (1982) 295, DOI: 10.1016/0370-2693(82)90373-2

The Unpredictability of Quantum Gravity.

S.W. Hawking (Cambridge U.). Print-83-0017 (CAMBRIDGE). May 1982. 29 pp. Published in Commun.Math.Phys. 87 (1982) 395-415, DOI: 10.1007/BF01206031

Bubble Collisions in the Very Early Universe.

S.W. Hawking, I.G. Moss, J.M. Stewart (Cambridge U.). Print-82-0180 (CAMBRIDGE). Mar 1982. 33 pp. Published in Phys.Rev. D26 (1982) 2681, DOI: 10.1103/PhysRevD.26.2681

Supercooled Phase Transitions in the Very Early Universe.

S.W. Hawking, I.G. Moss (Cambridge U.). Print-82-0181 (CAMBRIDGE). Dec 1981. 9 pp. Published in Phys.Lett. B110 (1982) 35, DOI: 10.1016/0370-2693(82)90946-7

The Boundary Conditions Of The Universe.

S.W. Hawking (Cambridge U.). PRINT-82-0179 (CAMBRIDGE). Sep 1981. 11 pp. Published in Pontif.Acad.Sci.Scrivaria 48 (1982) 563-574

The Cosmological Constant And The Weak Anthropic Principle.

S.W. Hawking (Cambridge U.). Print-82-0177 (CAMBRIDGE). Aug 1981. 9 pp. Published in In *London 1981, Proceedings, Quantum Structure Of Space and Time*, 423-432

Is The End In Sight For Theoretical Physics?.

S.W. Hawking (Cambridge U.). PRINT-81-0004 (CAMBRIDGE). Jan 1981. 17 pp. Published in Phys.Bull. 32 (1981) 15-17

The Loss Of Quantum Coherence Due To Virtual Black Holes.

S.W. Hawking (Cambridge U.). 1981. Published in In *Moscow 1981, Proceedings, Quantum Gravity*, 19-28

Why Is The Apparent Cosmological Constant Zero? (talk).

S.W. Hawking (Cambridge U.). 1981. Published in In *Muenchen 1981, Proceedings, Unified Theories Of Elementary Particles*, 167-175

Superspace And Supergravity. Proceedings, Nuffield Workshop, Cambridge, Uk, June 16 - July 12, 1980.

S.W. Hawking, (ed.), M. Rocek, (ed.). 1981. Published in Cambridge, Uk: Univ. Pr. (1981) 527p

Interacting Quantum Fields Around A Black Hole.

S.W. Hawking (Cambridge U.). Print-81-0251 (CAMBRIDGE). Dec 1980. 40 pp. Published in Commun.Math.Phys. 80 (1981) 421, DOI: 10.1007/BF01208279

Acausal Propagation In Quantum Gravity.

S.W. Hawking (Cambridge U.). PRINT-80-0866 (CAMBRIDGE), C80-04-15. Apr 1980. 22 pp. Published in In *Oxford 1980, Proceedings, Quantum Gravity 2*, 393-415

The Path Integral Approach To Quantum Gravity.

S.W. Hawking (Cambridge U.). 1980. Published in In *Hawking, S.W., Israel, W.: General Relativity*, 746-789

Introductory Survey.

S.W. Hawking (Cambridge U.), W. Israel (Alberta U.). 1980. Published in In *Hawking, S.W., Israel, W.: General Relativity*, 1-23

Quantum Gravitational Bubbles.

S.W. Hawking, Don N. Page, C.N. Pope (Cambridge U.). Print-80-0053 (CAMBRIDGE). Oct 1979. 33 pp. Published in Nucl.Phys. B170 (1980) 283-306, DOI: 10.1016/0550-3213(80)90151-0

decade#toggle"> 1970's

Yang-mills instantons and the s matrix..

S.W. Hawking, C.N. Pope (Cambridge U.). Print-79-0654 (CAMBRIDGE). Apr 1979. 32 pp. Published in Nucl.Phys. B161 (1979) 93, DOI: 10.1016/0550-3213(79)90128-7

Space-Time Foam.

S.W. Hawking (Cambridge U.). Print-79-0038 (CAMBRIDGE). Jan 1979. 24 pp. Published in Nucl.Phys. B144 (1978) 349-362, DOI: 10.1016/0550-3213(78)90375-9

Gravitational Multi – Instantons.

G.W. Gibbons, S.W. Hawking (Cambridge U.). Print-79-0042 (CAMBRIDGE). Jan 1979. 6 pp. Published in Phys.Lett. B78 (1978) 430, DOI: 10.1016/0370-2693(78)90478-1

Symmetry Breaking By Instantons In Supergravity.

S.W. Hawking, C.N. Pope (Cambridge U.). Print-79-0043 (CAMBRIDGE). Jan 1979. 22 pp. Published in Nucl.Phys. B146 (1978) 381, DOI: 10.1016/0550-3213(78)90073-1

The Propagation Of Particles In Space-time Foam.

S.W. Hawking, Don N. Page, C.N. Pope (Cambridge U.). 1979. Published in Phys.Lett. B86 (1979) 175-178, DOI: 10.1016/0370-2693(79)90812-8

Classification of Gravitational Instanton Symmetries.

G.W. Gibbons, S.W. Hawking (Cambridge U.). 1979. Published in Commun.Math.Phys. 66 (1979) 291-310, DOI: 10.1007/BF01197189

Relativity Today.

S. Hawking (Cambridge U.), W. Israel (Alberta U.). 1979. Published in New Sci. 81 (1979) 761-763

General Relativity. An Einstein Centenary Survey Pt 1.

S.W. Hawking (Cambridge U.), W. Israel (Alberta U.). 1979. Published in Cambridge, United Kingdom: Univ.Pr.(1979) 919p

Theoretical Advances In General Relativity.

S.W. Hawking (Cambridge U.). Print-79-0595 (CAMBRIDGE). Nov 1978. 16 pp.

Euclidean Quantum Gravity.

Stephen W. Hawking (Cambridge U.). PRINT-78-0745 (CAMBRIDGE), C78-07-10.1-2. Jul 1978. 30 pp. Published in NATO Adv.Study Inst.Ser.B Phys. 44 (1979) 145

Path Integrals and the Indefiniteness of the Gravitational Action.

G.W. Gibbons (Munich, Max Planck Inst. & Cambridge U.), S.W. Hawking, M.J. Perry (Cambridge U.). PRINT-78-0375 (CAMBRIDGE). Apr 1978. 14 pp. Published in Nucl.Phys. B138 (1978) 141, DOI: 10.1016/0550-3213(78)90161-X

Quantum Gravity and Path Integrals.

S.W. Hawking (Cambridge U. & Caltech). 1978. Published in Phys.Rev. D18 (1978) 1747-1753, DOI: 10.1103/PhysRevD.18.1747

Generalized Spin Structures in Quantum Gravity.

S.W. Hawking, C.N. Pope (Cambridge U.). Print-78-0374 (CAMBRIDGE). Nov 1977. 6 pp. Published in Phys.Lett. B73 (1978) 42-44, DOI: 10.1016/0370-2693(78)90167-3

Cosmological Event Horizons, Thermodynamics, and Particle Creation.

G.W. Gibbons, S.W. Hawking (Cambridge U.). 1977. Published in Phys.Rev. D15 (1977) 2738-2751, DOI: 10.1103/PhysRevD.15.2738

The Quantum Mechanics of Black Holes.

S.W. Hawking. 1977. Published in Sci.Am. 236 (1977) 34-49, DOI: 10.1038/scientificamerican0177-34

Black Holes and Unpredictability.

S.W. Hawking (Cambridge U.). PRINT-77-0292 (CAMBRIDGE). Dec 1976. 6 pp.Published in Phys.Bull. 29 (1978) 23-24

Gravitational Instantons.

S.W. Hawking (Cambridge U.). Print-77-0294 (CAMBRIDGE). Dec 1976. 8 pp. Published in Phys.Lett. A60 (1977) 81, DOI: 10.1016/0375-9601(77)90386-3

Zeta Function Regularization of Path Integrals in Curved Space-Time.

S.W. Hawking (Cambridge U.). PRINT-77-0293 (CAMBRIDGE). Dec 1976. 29 pp. Published in Commun.Math.Phys. 55 (1977) 133, DOI: 10.1007/BF01626516

Action Integrals and Partition Functions in Quantum Gravity.

G.W. Gibbons, S.W. Hawking (Cambridge U.). PRINT-76-0995 (CAMBRIDGE). Sep 1976. 14 pp. Published in Phys.Rev. D15 (1977) 2752-2756, DOI: 10.1103/PhysRevD.15.2752

Gamma rays from primordial black holes.

Don N. Page, S.W. Hawking. May 1976. 7 pp. Published in Astrophys.J. 206 (1976) 1-7, DOI: 10.1086/154350

Breakdown of Predictability in Gravitational Collapse.

S.W. Hawking (Cambridge U. & Caltech). 1976. Published in Phys.Rev. D14 (1976) 2460-2473, DOI: 10.1103/PhysRevD.14.2460

Path Integral Derivation of Black Hole Radiance.

J.B. Hartle, S.W. Hawking (UC, Santa Barbara & Caltech & Cambridge U.). 1976. Published in Phys.Rev. D13 (1976) 2188-2203, DOI: 10.1103/PhysRevD.13.2188

Black Holes and Thermodynamics.

S.W. Hawking (Caltech & Cambridge U.). 1976. Published in Phys.Rev. D13 (1976) 191-197, DOI: 10.1103/PhysRevD.13.191

A New Topology for Curved Space-Time Which Incorporates the Causal, Differential, and Conformal Structures.

S.W. Hawking (Cambridge U. & Caltech), A.R. King, P.J. Mccarthy. 1976. Published in J.Math.Phys. 17 (1976) 174-181, DOI: 10.1063/1.522874

Particle Creation by Black Holes.

S.W. Hawking (Cambridge U.). Aug 1975. 22 pp. Published in Commun.Math.Phys. 43 (1975) 199-220, Erratum-ibid. 46 (1976) 206-206, DOI: 10.1007/BF02345020

Black hole explosions.

S.W. Hawking (Cambridge U.). Mar 1974. 2 pp. Published in Nature 248 (1974) 30-31, DOI: 10.1038/248030a0

Black holes in the early Universe.

Bernard J. Carr, S.W. Hawking (Cambridge U., Inst. of Astron. & Cambridge U., DAMTP). Feb 1974. 17 pp. Published in Mon.Not.Roy.Astron.Soc. 168 (1974) 399-415. DOI: 10.1093/mnras/168.2.399

Causally continuous space-times.

S.W. Hawking, R.K. Sachs. 1974. Published in Commun.Math.Phys. 35 (1974) 287-296, DOI: 10.1007/BF01646350

A Variational principle for black holes.

S.W. Hawking. 1973. Published in Commun.Math.Phys. 33 (1973) 323-334, DOI: 10.1007/BF01646744

The Four laws of black hole mechanics.

James M. Bardeen (Yale U.), B. Carter, S.W. Hawking (Cambridge U.). 1973. Published in Commun.Math.Phys. 31 (1973) 161-170, DOI: 10.1007/BF01645742

The Large scale structure of space-time.

S.W. Hawking, G.F.R. Ellis. 1973. 391 pp. Published in Cambridge University Press, Cambridge, 1973. ISBN-13: 978-0521099066

The rotation and distortion of the universe.

C.B. Collins, S.W. Hawking. Jan 1973, Published in Mon.Not.Roy.Astron.Soc. 162 (1973) 307-320

Why is the Universe isotropic?.

C.B. Collins, S.W. Hawking (Cambridge U., DAMTP & Cambridge U.). Sep 1972. 18 pp. Published in Astrophys.J. 180 (1973) 317-334, DOI: 10.1086/151965

Solutionsof the Einstein-Maxwell equations with many black holes.

J.B. Hartle, S.W. Hawking. Jun 1972. Published in Commun.Math.Phys. 26 (1972) 87-101, DOI: 10.1007/BF01645696

Energy and angular momentum flow into a black hole.

S.W. Hawking (Cambridge U., DAMTP), J.B. Hartle (UC, Santa Barbara). 1972. Published in Commun.Math.Phys. 27 (1972) 283-290, DOI: 10.1007/BF01645515

Black holes in the Brans-Dicke theory of gravitation.

S.W. Hawking (Cambridge U.). 1972. Published in Commun.Math.Phys. 25 (1972) 167-171, DOI: 10.1007/BF01877518

Theory of the detection of short bursts of gravitational radiation.

G.W. Gibbons, S.W. Hawking (Cambridge U., DAMTP). 1972. Published in Phys.Rev. D4 (1971) 2191-2197, DOI: 10.1103/PhysRevD.4.2191

Black holes in general relativity.

S.W. Hawking (Cambridge U.). Oct 1971. Published in Commun.Math.Phys. 25 (1972) 152-166, DOI: 10.1007/BF01877517

Gravitational radiation from colliding black holes.

S.W. Hawking (Cambridge U.). Mar 1971. Published in Phys.Rev.Lett. 26 (1971) 1344-1346, DOI: 10.1103/PhysRevLett.26.1344

Evidence for black holes in binary star systems.

S.W. Hawking, G.W. Gibbons. 1971. Published in Nature 232 (1971) 465, DOI: 10.1038/232465a0

The Definition and occurrence of singularities in general relativity.

Stephen Hawking. 1971. Published in Lect.Notes Math. 209 (1971) 275-279

Stable and generic properties in general relativity.

Stephen Hawking (Cambridge U., Inst. of Astron.). 1971. Published in Gen.Rel.Grav. 1 (1971) 393-400, DOI: 10.1007/BF00759218

Gravitationally collapsed objects of very low mass.

Stephen Hawking. 1971. Published in Mon.Not.Roy.Astron.Soc. 152 (1971) 75. DOI: 10.1093/mnras/152.1.75

The Singularities of gravitational collapse and cosmology.

S.W. Hawking (Cambridge U.), R. Penrose (Birkbeck Coll.). Jan 1970. 20 pp. Published in Proc.Roy.Soc.Lond. A314 (1970) 529-548, DOI: 10.1098/rspa.1970.0021

The conservation of matter in general relativity.

S. Hawking (Cambridge U., DAMTP). 1970. Published in Commun.Math.Phys. 18 (1970) 301-306, DOI: 10.1007/BF01649448

decade#toggle"> 1960's

Singularities in collapsing stars and universes..

Stephen Hawking, Dennis Sciama. 1969. Published in Comments Astrophys. Space Phys. 1 (1969) 1

On the Rotation of the universe.

S.W. Hawking (Cambridge U., Inst. of Astron.). Sep 1968. 13 pp. Published in Mon.Not.Roy.Astron.Soc. 142 (1969) 129-141.

Gravitational radiation in an expanding universe.

Stephen Hawking (Cambridge U., DAMTP). Apr 1968. Published in J.Math.Phys. 9 (1968) 598-604, DOI: 10.1063/1.1664615

The Cosmic black body radiation and the existence of singularities in our universe.

G.F.R. Ellis, Stephen Hawking. 1968. Published in Astrophys.J. 152 (1968) 25, DOI: 10.1086/149520

The Existence of cosmic time functions.

Stephen Hawking (Cambridge U., DAMTP). 1968. Published in Proc.Roy.Soc.Lond. A308 (1968) 433-435. DOI: 10.1098/rspa.1969.0018

The occurrence of singularities in cosmology. III. Causality and singularities.

Stephen Hawking (Cambridge U., DAMTP). 1967. Published in Proc.Roy.Soc.Lond. A300 (1967) 187-201, DOI: 10.1098/rspa.1967.0164

Perturbations of an expanding universe.

S.W. Hawking (Cambridge U., DAMTP). Feb 1966. 11 pp. Published in Astrophys.J. 145 (1966) 544-554, DOI: 10.1086/148793

Singularities in the universe.

S.W. Hawking. 1966. Published in Phys.Rev.Lett. 17 (1966) 444-445, DOI: 10.1103/PhysRevLett.17.444

Helium production in anisotropic big bang universes.

Stephen Hawking, J.R. Tayler (Cambridge U., DAMTP). 1966. Published in Nature 209 (1966) 1278-1279, DOI: 10.1038/2091278a0

The Occurrence of singularities in cosmology.

Stephen Hawking (Cambridge U., DAMTP). 1966. Published in Proc.Roy.Soc.Lond. A294 (1966) 511-521, DOI: 10.1098/rspa.1966.0221

The Occurrence of singularities in cosmology. II.

Stephen Hawking (Cambridge U., DAMTP). 1966. Published in Proc.Roy.Soc.Lond. A295 (1966) 490-493, DOI: 10.1098/rspa.1966.0255

Singularities and the geometry of space-time.

Stephen Hawking. 1966. DOI: 10.1140/epjh/e2014-50013-6

Properties of Expanding Universes.

Stephen Hawking, PhD Thesis. 1965, DOI: 10.17863/CAM.11283

On the Hoyle-Narlikar theory of gravitation.

Stephen Hawking (Cambridge U., DAMTP). Feb 1965. Published in Proc.Roy.Soc.Lond. A286 (1965) 313-319, DOI: 10.1098/rspa.1965.0146

Occurrence of singularities in open universes.

Stephen Hawking (Cambridge U., DAMTP). 1965. Published in Phys.Rev. ett. 15 (1965) 689-690, DOI: 10.1103/PhysRevLett.15.689

Singularities in homogeneous world models.

Stephen Hawking, G.F.R. Ellis (Cambridge U., DAMTP & Cambridge U.). Jun 1965. Published in Phys.Lett. 17 (1965) 246-247, DOI: 10.1016/0031-9163(65)90510-X