# New mathematical formulation means huge paradigm shift in physics would not be necessary

Stephen Hawking’s black hole information paradox has bedevilled scientists for half a century and led some to question the fundamental laws of physics. Now scientists say they may have resolved the infamous problem by showing that black holes have a property known as “quantum hair”.

If correct, this would mark a momentous advance in theoretical physics.

Prof Xavier Calmet, of the University of Sussex, who led the work, said that after working on the mathematics behind the problem for a decade, his team made a rapid advance last year that gave them confidence that they had finally cracked it.

“It was generally assumed within the scientific community that resolving this paradox would require a huge paradigm shift in physics, forcing the potential reformulation of either quantum mechanics or general relativity,” said Calmet. “What we found – and I think is particularly exciting – is that this isn’t necessary.”

Hawking’s paradox boils down to the following: the rules of quantum physics state that information is conserved. Black holes pose a challenge to this law because once an object enters a black hole, it is essentially gone for good – along with any information encoded in it. Hawking identified this paradox and for decades it has continued to confound scientists.

There have been innumerable proposed solutions, including a “firewall theory” in which information was assumed to burn up before entering the black hole, the “fuzzball theory” in which black holes were thought to have indistinct boundaries, and various exotic branches of string theory. But most of these proposals required rewriting of the laws of quantum mechanics or Einstein’s theory of gravity, the two pillars of modern physics.

By contrast, the quantum hair theorem claims to resolve the paradox by bridging the gap between general relativity and quantum mechanics using a new mathematical formulation.

The name is a nod to the view, based on classical physics, that black holes can be viewed as surprisingly simple objects, defined only by their mass and speed of rotation. The prediction of bald, featureless black holes has been nicknamed the “no-hair theorem” since the 1970s.

Calmet and his collaborators think the black hole is more complex – or hairy. As matter collapses into a black hole, they suggest, it leaves a faint imprint in its gravitational field. This imprint is referred to as “quantum hair” and, the authors say, would provide the mechanism by which information is preserved during the collapse of a black hole. Under this theory, two black holes with identical masses and radii, but with different internal composition, would have very subtle differences in their gravitational fields.

“Our solution doesn’t require any speculative idea; instead our research demonstrates that the two theories can be used to make consistent calculations for black holes and explain how information is stored without the need for radical new physics,” said Calmet.

There is no obvious way to test the theory through astronomical observations – the gravitational fluctuations would be too tiny to be measurable. But the theory is likely to come under robust scrutiny from the theoretical community.

Prof Toby Wiseman, a theoretical physicist at Imperial College London, described the paper as “a good bit of work”, but remained unconvinced that it resolved the decades-old paradox.

Crucially, he said, the paper suggested it may be possible to get some additional information about what was inside the black hole – but did not show that the phenomenon could account for the entirety of the information apparently lost. “That they haven’t shown and that’s the crux of the paradox,” he said.

“My feeling is that to really resolve this paradox you have to fully understand how quantum mechanics and gravity come together,” he said. “They’re looking at small corrections, but not the full combination of the two.”

Calmet said: “When you have a big claim you have to back it up. It’s going to take some time for people to fully accept this. The paradox has been around for a long time and you’ve got very famous people all over the world who’ve been working on this for years.”

The work is published in the journal Physical Review Letters.