What happens to information after it has passed beyond the event horizon of a black hole? There have been suggestions that the geometry of wormholes might help us solve this vexing problem – but the math has been tricky, to say the least.
In a new paper, an international team of physicists has found a workaround for better understanding how a collapsing black hole can avoid breaking the fundamental laws of quantum physics (more on that in a bit).
Although highly theoretical, the work suggests there are likely things we are missing in the quest to resolve general relativity with quantum mechanics.
“We discovered a new spacetime geometry with a wormhole-like structure that had been overlooked in conventional computations,” says physicist Kanato Goto of Cornell University and RIKEN in Japan.
“Entropy computed using this new geometry gives a completely different result.”
The black hole information paradox is one of the unresolved tensions between Einstein’s theory of general relativity and quantum mechanics.
Under general relativity, the event horizon of a black hole is a point of no return. Everything that passes beyond that critical point is inexorably slurped into the black hole’s gravity well, and no speed in the Universe, not even that of light in a vacuum, is sufficient for escape velocity. It’s gone, that’s it. Kaput. Irretrievable.
Then along came Stephen Hawking in the 1970s, suggesting that, when quantum mechanics is taken under consideration, black holes could emit radiation after all.
This, according to theory, occurs as a result of the black hole’s interference with surrounding particles’ wave-like properties, effectively making it ‘glow’ with a temperature that gets hotter as the black hole gets smaller.
Eventually, this glow should make a black hole shrink to nothing.
“This is called black hole evaporation because the black hole shrinks, just like an evaporating water droplet,” Goto explains.
Since the ‘glow’ doesn’t look like what went into the black hole in the first place, it would appear that whatever entered into the evaporated black hole is gone for good. But according to quantum mechanics, information cannot simply vanish from the Universe. Many physicists have explored the possibility that somehow, that information is encoded in Hawking radiation.
Goto and his team wanted to mathematically explore this idea by computing the entropy of Hawking radiation around a black hole. That’s the measure of disorder in a system, and can be used to diagnose information loss in Hawking radiation.
According to a 1993 paper by physicist Don Page, if disorder reverses and entropy drops down to zero as a black hole vanishes, the paradox of the missing information should be avoided. Unfortunately, there’s nothing in quantum mechanics that would allow this reversal to happen.
Enter the wormhole, or at least a mathematical replica of one under very specific models of the Universe. This is a connection between two regions of a curved sheet of spacetime, a bit like a bridge across a ravine.
Thinking of it this way in conjunction with black holes gives us a different means of calculating the entropy of Hawking radiation, Goto says.
“A wormhole connects the interior of the black hole and the radiation outside, like a bridge,” he explains.
When the team performed their calculations using the wormhole model, their results matched the Page entropy curve. This suggests that information hoovered beyond the event horizon of a black hole might not be lost forever after all.
But there are, of course, still some questions that remain. Until these are answered, we can’t consider the black hole information paradox definitively resolved.
“We still don’t know the basic mechanism of how information is carried away by the radiation,” Goto says. “We need a theory of quantum gravity.”
The research has been published in the Journal of High Energy Physics.