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Stephen Hawking's final paper published, tackles famous paradox

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Enlarge / Artist’s depiction of a black hole. These strange objects could hold the key to a theory of quantum gravity.

When famed physicist Stephen Hawking passed away earlier this year, he left a scientific legacy that included one of the knottiest paradoxes in modern theoretical physics. Now his final paper has just been published, revisiting the question of whether information can be retrieved from a black hole or whether it is lost forever. The paper posits that information can be stored in a halo of “soft hair” surrounding a black hole.

Once upon a time, physicists believed that black holes had no hair. “We can often tell people apart by looking at their hair, but black holes seemed to be completely bald,” co-author Malcolm Perry of the University of Cambridge writes in The Guardian. That is, all you needed to describe black holes mathematically was their mass and their spin. So there would be no noticeable change if you threw something into a black hole—nothing that would provide a clue as to what that object might have been. That information is lost.

But in 1974, Hawking realized that black holes also have a temperature, and if so, they had to produce some kind of thermal radiation. So black holes must also have entropy—technically, a means of determining how many different ways you can rearrange the atoms of an object and still have it look pretty much the same. Hawking was the first to calculate that entropy. He also introduced the notion of “Hawking radiation.”

Stephen Hawking in Princeton, New Jersey, October 1979.
Enlarge / Stephen Hawking in Princeton, New Jersey, October 1979.
Santi Visalli/Getty Images

In quantum mechanics, empty space is not really empty. Matter/anti-matter pairs of so-called “virtual” particles are constantly popping into existence and annihilating just as quickly. But if a pair pops up near the event horizon of a black hole and one of the pair falls in, the black hole will emit a tiny bit of energy, decreasing its mass by a corresponding amount. Over time, the black hole will evaporate. The smaller the black hole, the more quickly it disappears.

Birth of a paradox

The next part of the story starts with a bet in 1991. Hawking and Caltech physicist Kip Thorne bet John Preskill (also at Caltech) that information that falls into a black hole is destroyed, and you can never get it back. Preskill thought it might be preserved in the Hawking radiation as the black hole evaporates. Hawking and Thorne counter-argued that any information thus released would be so badly scrambled that it would be useless. For all practical purposes, the information would be lost.

In 2004, the paradox seemed to be resolved when physicists proposed the notion of black hole complementarity. Under this scenario, information that falls into a black hole simultaneously reflects back out. No single observer can be both inside and outside the event horizon, so no one can witness both events at the same time. There were still some nagging questions, but the argument convinced Hawking, and he conceded the bet. Preskill received a copy of Total Baseball: The Ultimate Baseball Encyclopedia as his prize, “from which information can be retrieved at will.”

But a 2012 paper revisiting the paradox threw yet another spanner into the works. While pondering possible mechanisms for getting information out of a black hole, the late Joseph Polchinski (University of Santa Barbara) and three colleagues realized that three much-believed fundamental postures of physics could not all be true. One had to be wrong, and they believed it was the nature of the event horizon.

In-falling observers would be burnt to a crisp by a literal wall of fire at the horizon.

Conventional wisdom held that when someone crossed the event horizon, they would notice nothing amiss. It was only as they moved closer to the singularity that the extreme gravitational forces would rip them to shreds (Thorne called this being “spaghettified”). Physicists call this the “No Drama” scenario. But Polchinski et al. said that in-falling observers would be burnt to a crisp by a literal wall of fire at the horizon.

It’s similar to a proposal by The Ohio State University string theorist Samir Mathur a few years before. Mathur argued that black holes are not empty pits but packed full of strings (the fundamental units of string theory), with an actual surface like a star or planet. Polchinski’s firewall is essentially a hot fuzzball.

<a href="https://cdn.arstechnica.net/wp-content/uploads/2018/10/hawking-1200.jpg" class="enlarge" data-height="801" data-width="1200" alt="When not stumping physicists with paradoxes, Hawking liked to make cameos on popular TV shows. Here he is on the set of The Big Bang Theory with Sheldon Cooper (Jim Parsons).”><img alt="When not stumping physicists with paradoxes, Hawking liked to make cameos on popular TV shows. Here he is on the set of The Big Bang Theory with Sheldon Cooper (Jim Parsons).” src=”https://cdn.arstechnica.net/wp-content/uploads/2018/10/hawking-1200-640×427.jpg” width=”640″ height=”427″ srcset=”https://cdn.arstechnica.net/wp-content/uploads/2018/10/hawking-1200.jpg 2x”>
Enlarge / When not stumping physicists with paradoxes, Hawking liked to make cameos on popular TV shows. Here he is on the set of The Big Bang Theory with Sheldon Cooper (Jim Parsons).
CBS Photo Archive/Getty Images

But this is just the most straightforward solution to resolve the paradox. Physicists loathe to sacrifice No Drama have proposed all kinds of alternative solutions in the ensuing years. Hawking did so, too, in a two-page 2014 paper posted to the preprint site arXiv.org. It wasn’t a technical paper, with zero equations, but rather a summary of a talk he’d given at a conference the prior year.

Hawking suggested that perhaps the event horizon is not some definite point of no return beyond which nothing could escape a black hole. Maybe there was just an “apparent horizon” that temporarily confined the information. The information is not stored in the interior of the black hole but in its boundary: the event horizon.

Black holes with soft hair

Hawking’s final paper builds on that prior insight. As Perry writes, he and a third co-author, Harvard’s Andrew Strominger, found a gap in the mathematical argument concluding that black holes had no hair. In their new paper, they’ve come up with a new way to calculate the entropy of a black hole. They show that you can record the entropy of a black hole in the photons (particles of light) bouncing around the event horizon. Those photons make up a kind of halo around the black hole that the authors have dubbed “soft hair.” And that soft hair can account for the entropy.

“We don’t know that Hawking entropy accounts for everything you could possibly throw at a black hole.”

Hawking died before the paper could be published. But Perry told BBC News that he had called his colleague just before that—unaware of how ill Hawking had become—and told him via loudspeaker of their conclusions. “When I explained it, he simply produced an enormous smile,” Perry said.

Reactions from the community of theoretical physicists have been guardedly positive thus far. “This paper proposes a way to understand entropy for astrophysical black holes based on symmetries of the event horizon,” Marika Taylor, a former student of Hawking’s and a physicist at Southampton University, told The Guardian. “The authors have to make several non-trivial assumptions, so the next steps will be to show that these assumptions are valid.”

The authors concede that this is not a complete solution to the black hole information paradox, but it provides useful insight. “We don’t know that Hawking entropy accounts for everything you could possibly throw at a black hole,” Perry told The Guardian, adding in his own accompanying essay, “While we have not solved the information paradox, we hope that we have paved the way [to a solution].”

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