In 1963, the mathematician Roy Kerr found a solution to Einstein’s equations that precisely described the space-time outside what we now call a rotating black hole.

(The term wouldn’t be coined for a few more years.) In the nearly six decades since his achievement, researchers have tried to show that these so-called Kerr black holes are stable.

What that means, explained Jérémie Szeftel, a mathematician at Sorbonne University, “is that if I start with something that looks like a Kerr black hole and give it a little bump” — by throwing some gravitational waves at it, for instance — “what you expect, far into the future, is that everything will settle down, and it will once again look exactly like a Kerr solution.”.

In a 912-page paper posted online on May 30, Szeftel, Elena Giorgi of Columbia University and Sergiu Klainerman of Princeton University have proved that slowly rotating Kerr black holes are indeed stable.

The space-time outside the black hole would then be so severely distorted that the Kerr solution would no longer prevail.

The argument goes roughly like this: First, the researchers assume the opposite of what they’re trying to prove, namely that the solution does not exist forever — that there is, instead, a maximum time after which the Kerr solution breaks down.

So far, stability has only been proved for slowly rotating black holes — where the ratio of the black hole’s angular momentum to its mass is much less than 1.

It has not yet been demonstrated that rapidly rotating black holes are also stable.

Given that only one step in their long proof rests on the assumption of low angular momentum, Klainerman said he would “not be surprised at all if, by the end of the decade, we will have a full resolution of the Kerr [stability] conjecture.”.

Looming beyond this problem is a much bigger one called the final state conjecture, which basically holds that if we wait long enough, the universe will evolve into a finite number of Kerr black holes moving away from each other

Yet it also illustrates an essential truth about Kerr black holes: They are destined to command the attention of mathematicians for years, if not decades, to come