"A black hole has no hair."
That mysterious, koan-like statement by the theorist and legendary phrasemaker John Archibald Wheeler of Princeton has stood for half a century as one of the brute pillars of modern physics.
It describes the ability of nature, according to classical gravitational equations, to obliterate most of the attributes and properties of anything that falls into a black hole, playing havoc with science's ability to predict the future and tearing at our understanding of how the universe works.
Now it seems that statement might be wrong.
Recently, theoretical physicist Stephen Hawking, who has spent his entire career battling a form of Lou Gehrig's disease, wheeled across the stage in Harvard's hoary, wood-panelled Sanders Theatre to do battle with the black hole. It is one of the most fearsome demons ever conjured by science, and one partly of his own making: a cosmic pit so deep and dense and endless that it was long thought that nothing - not even light, not even a thought - could ever escape.
They are not the eternal prisons they were once thought. If you feel you are trapped in a black hole, don't give up. There is a way out.
STEPHEN HAWKING, who says he and his colleagues have found a clue pointing the way out of black holes.
But Hawking was there to tell us not to be so afraid.
In a paper to be published in Physical Review Letters, Hawking and his colleagues Andrew Strominger of Harvard and Malcolm Perry of Cambridge University in England say they have found a clue pointing the way out of black holes.
"They are not the eternal prisons they were once thought," Hawking said in his famous robot voice, now processed through a synthesiser. "If you feel you are trapped in a black hole, don't give up. There is a way out."
Black holes are the most ominous prediction of Einstein's general theory of relativity: Too much matter or energy concentrated in one place would cause space to give way, swallowing everything inside like a magician's cloak.
An eternal prison was the only metaphor scientists had for these monsters until 40 years ago, when Hawking turned black holes upside down - or perhaps inside out.
His equations showed that black holes would not last forever. Over time, they would "leak" and then explode in a fountain of radiation and particles. Ever since, the burning question in physics has been: When the black hole finally goes, does it give up the secrets of everything that fell in?
Hawking's calculation was, and remains, hailed as a breakthrough in understanding the connection between gravity and quantum mechanics, between the fabric of space and the subatomic particles that live inside it - the large and the small in the universe.
But there was a hitch. By Hawking's estimation, the radiation coming out of the black hole as it fell apart would be random. As a result, most of the "information" about what had fallen in - all of the attributes and properties of the things sucked in, whether elephants or donkeys, Volkswagens or Cadillacs - would be erased.
In a riposte to Einstein's famous remark that God does not play dice, Hawking said in 1976 that "God not only plays dice with the universe, but sometimes throws them where they can't be seen".
But his calculation violated a tenet of modern physics: that it is always possible in theory to reverse time, run the proverbial film backward and reconstruct what happened in, say, the collision of two cars or the collapse of a dead star into a black hole.
The universe, like a kind of supercomputer, is supposed to be able to keep track of whether one vehicle was a green pick-up truck and the other was a red Porsche, or whether one was made of matter and the other anti-matter. These things may be destroyed, but their "information" - their essential physical attributes - should live forever.
In fact, the information seemed to be lost in the black hole, according to Hawking, as if part of the universe's memory chip had been erased. According to this theorem, only information about the mass, charge and angular momentum of what went in would survive.
Nothing about whether it was anti-matter or matter, male or female, sweet or sour.
A war of words and ideas ensued. The information paradox, as it is known, was no abstruse debate, as Hawking pointed out from the stage of the Sanders Theatre in April. Rather, it challenged foundational beliefs about what reality is and how it works.
If the rules break down in black holes, they may be lost in other places as well, he warned.
If foundational information disappears into a gaping maw, the notion of a "past" itself may be in jeopardy - we couldn't even be sure of our own histories. Our memories could be illusions.
"It's the past that tells us who we are. Without it, we lose our identity," he said.
Fortunately for historians, Hawking conceded defeat in the black hole information debate 10 years ago, admitting that advances in string theory, the so-called theory of everything, had left no room in the universe for information loss.
At least in principle, then, he agreed, information is always preserved - even in the smoke and ashes when you, say, burn a book. With the right calculations, you should be able to reconstruct the patterns of ink, the text.
Hawking paid off a bet with John Preskill, a Caltech physicist, with a baseball encyclopaedia, from which information can be easily retrieved.
NOT BALD AFTER ALL
But neither Hawking nor anybody else was able to come up with a convincing explanation for how that happens and how all this "information" escapes from the deadly erasing clutches of a black hole.
Indeed, a group of physicists four years ago tried to figure it out and suggested controversially that there might be a firewall of energy just inside a black hole that stops anything from getting out or even into a black hole.
The new results do not address that issue. But they do undermine the famous notion that black holes have "no hair" - that they are shorn of the essential properties of the things they have consumed.
About four years ago, Strominger started noodling around with theoretical studies about gravity dating to the early 1960s.
Interpreted in a modern light, the papers - published in 1962 by Hermann Bondi, M.G.J. van der Burg, A.W.K. Metzner and Rainer Sachs, and in 1965 by Steven Weinberg, later a recipient of the Nobel Prize - suggested that gravity was not as ruthless as Wheeler had said.
Looked at from the right vantage point, black holes might not be bald at all.
The right vantage point is not from a great distance in space - the normal assumption in theoretical calculations - but from a far distance in time, the far future, technically known as "null infinity".
"Null infinity is where light rays go if they are not trapped in a black hole," Strominger tried to explain over coffee in Harvard Square recently.
From this point of view, you can think of light rays on the surface of a black hole as a bundle of straws all pointing outward, trying to fly away at the speed of, of course, light. Because of the black hole's immense gravity, they are stuck.
But the individual straws can slide inward or outward along their futile tracks, slightly advancing or falling back, under the influence of incoming material. When a particle falls into a black hole, it slides the straws of light back and forth, a process called a supertranslation.
That leaves a telltale pattern on the horizon, the invisible boundary that is the point of no return of a black hole - a halo of "soft hair", as Strominger and his colleagues put it. That pattern, like the pixels on your iPhone or the wavy grooves in a vinyl record, contains information about what has passed through the horizon and disappeared.
"One often hears that black holes have no hair," Strominger and a post-doctoral researcher, Alexander Zhiboedov, wrote in a 2014 paper. Not true: "Black holes have a lush infinite head of supertranslation hair."
For years, he and Strominger and a few others had got together to work in seclusion at a Texas ranch owned by the oilman and fracking pioneer George Mitchell. Because Hawking was discouraged from flying, in April 2014 the retreat was in Hereford, Britain.
It was there that Hawking first heard about soft hair - and was very excited. He, Strominger and Perry began working together.
In Stockholm later that year, he made a splash when he announced that a resolution to the information paradox was at hand - somewhat to the surprise of Strominger and Perry, who have been trying to maintain an understated stance.
Although information gets hopelessly scrambled, Hawking declared that it "can be recovered in principle, but it is lost for all practical purposes".
In January, Hawking, Strominger and Perry posted a paper online titled Soft Hair On Black Holes, laying out the basic principles of their idea. In the paper, they are at pains to admit that knocking the pins out from under the no-hair theorem is a far cry from solving the information paradox. But it is progress.
Their work suggests that science has been missing something fundamental about how black holes evaporate, Strominger said. And now they can sharpen their questions. "I hope we have the tiger by the tail," he said.
Whether or not soft hair is enough to resolve the information paradox, nobody really knows. Reaction from other physicists has been reserved.
Juan Maldacena of the Institute for Advanced Study in Princeton, New Jersey, said of the new proposal: "Its significance for the black hole information problem remains to be seen. But it is probable that it plays some role."
Strominger has serious street cred when it comes to black holes. In a celebrated calculation in 1996, he and Cumrun Vafa computed the information content of a black hole, verifying Hawking's famous conjecture that black holes explode.
Their work is still one of the greatest achievements of string theory, the vaunted and yet unproved theory of everything. If this estimate of the content in a black hole matches one made from supertranslations, physicists would arrive at a fundamental, new understanding of how they work.
But Strominger and Perry admit that they are not anywhere near doing that yet. In a new paper not yet released, Strominger said they had been able to show that information could also be encoded in the twisting of light beams trying to escape from the black hole, not just their sliding back and forth.
At Harvard in April, Hawking, who has a taste for dramatic statements, doubled down on his Stockholm declaration.
"When I wrote my paper 40 years ago, I thought the information would pass into another universe," he told me.
Now he thinks the information is stored on the black hole's horizon. "The information will be re-emitted when the black hole evaporates. My work with my colleagues Andy Strominger of Harvard and Malcolm Perry of Cambridge has shown us the mechanism for information retrieval from a black hole."
You could even get out of a black hole, at least in principle. Limits can always be transcended.
Hawking himself is proof enough.
He has long been confined to a wheelchair, yet raised three children, published the best-selling A Brief History Of Time, lost his voice to a tracheotomy, divorced, remarried, divorced again. He has become something of a pop icon. And he recently called Donald Trump a "demagogue".
He has survived several pneumonia episodes. Prior to his appearance in Boston, he arrived in New York on a Swiss ambulance airplane with a retinue that included nurses and an IT expert to keep his computer and voice synthesiser working. His intellect is perhaps exceeded only by his stubbornness.
Hawking and his colleagues worked in a hotel by day and were feted at night, including a party at the home of the media baron Rupert Murdoch.
The considerable expense was covered by Yuri Milner, a Russian philanthropist and entrepreneur, who wanted Hawking on hand to help announce a new project to see if we can fly iPhone-like spaceships to Alpha Centauri, the nearest star.
"What makes humans unique?" Hawking asked rhetorically during the ceremony atop One World Center. "Gravity keeps us down, but I flew here on an airplane. I lost my voice, but I can speak through a voice synthesiser."
"How do we transcend these limits?" he went on. "With our minds and our machines."
NEW YORK TIMES