The space-time outside what we now call a rotating black hole was described by Roy Kerr in 1963. For a while, the term wouldn't be used. Researchers have been trying to prove that the Kerr black holes are stable. If I start with something that looks like a Kerr black hole and give it a little bit of a boost, that's what I mean.
Thibault Damour, a physicist at the Institute of Advanced Scientific Studies, said that a mathematical instability would have posed a deep dilemma to theoretical physicists.
In a 912-page paper posted online on May 30, the three of them proved that Kerr black holes are stable. The work was done over a long period of time. The proof consists of a new work, an 800-page paper by the two authors, and three background papers that established various mathematical tools.
Demetrios Christodoulou, a mathematician at the Swiss Federal Institute of Technology, said that the new result is a milestone in the development of general relativity.
Shing-Tung Yau said the proof was the first major breakthrough in this area of general relativity since the early 1990s. He said it was a very difficult problem. The new paper has not yet been peer reviewed. He described the paper as complete and exciting.
Most explicit solutions to Einstein's equations, such as the one found by Kerr, are stationary. Black holes that are sitting there and never changing are not the black holes we see. To assess stability, researchers need to see what happens to the solutions that describe black holes as time goes on.
Imagine sound waves hitting a wine glass. The system settles down after the waves shake the glass. The glass could break if someone sings loudly enough and at a pitch that matches the resonance of the glass. They wondered if a resonance-type phenomenon could happen when a black hole is hit by waves.
Several possible outcomes were considered. The event horizon of a Kerr black hole could be crossed by a wave. The object would still be a black hole even if the mass and rotation were altered. The waves could swirl around the black hole before dissipating, like sound waves do after hitting a wineglass.
Or they could combine and wreak havoc. There is a chance that the waves will congregate outside of the black hole's event horizon. The Kerr solution would no longer work due to the distorted space-time outside the black hole. This could be a sign of trouble.
A proof by contradiction strategy was used by the mathematicians. The researchers assume that the solution does not exist forever and that there is a maximum time after which the Kerr solution breaks down. The partial differential equations that lie at the heart of general relativity are used to extend the solution beyond the purported maximum time. They show that regardless of what value is chosen, it can always be extended. The initial assumption is that the conjecture is true.
The work of others has been built upon by the others. We are the lucky ones because there have been four serious attempts. He wants the new paper to be seen as a triumph for the entire field.
Slowly rotating black holes are the only ones that have been proven to be stable. Black holes with rapid rotation are also stable. The researchers didn't know how small the ratio of inertia to mass has to be to ensure stability.
Klainerman said he would not be surprised if by the end of the decade we would have a full resolution of the Kerrstability conjecture.
He isn't quite so sanguine. It's true that the assumption applies to just one case, but it's a very important case. She said it will take a lot of work to get past that restriction.
If we wait long enough, the universe will evolve into a finite number of Kerr black holes that will move away from each other. The Kerr stability and other sub-conjectures are extremely challenging in their own right. "We don't know how to prove this," he said. That statement may sound pessimistic to some. It shows that Kerr black holes are destined to command the attention of mathematicians for a long time.
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