At Long Last, Mathematical Proof That Black Holes Are Stable

The spacetime outside 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 is a physicist at the Institute of Advanced Scientific Studies.

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 the new work, an 800-page paper by the two authors from the year 2021, 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 The new paper has not yet been peer reviewed.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 because of the distorted spacetime outside the black hole. This could be a sign of trouble.