In 1963, the mathematician Roy Kerr found a solution to Einstein's equations that precisely described the spacetime 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."
The opposite situation—a mathematical instability—"would have posed a deep conundrum to theoretical physicists and would have suggested the need to modify, at some fundamental level, Einstein's theory of gravitation," said Thibault Damour, a physicist at the Institute of Advanced Scientific Studies in France.
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 work is the product of a multiyear effort. The entire proof—consisting of the new work, an 800-page paper by Klainerman and Szeftel from 2021, plus three background papers that established various mathematical tools—totals roughly 2,100 pages in all.
The new result "does indeed constitute a milestone in the mathematical development of general relativity," said Demetrios Christodoulou, a mathematician at the Swiss Federal Institute of Technology Zurich.
[...] One reason the question of stability has remained open for so long is that most explicit solutions to Einstein's equations, such as the one found by Kerr, are stationary, Giorgi said. "These formulas apply to black holes that are just sitting there and never change; those aren't the black holes we see in nature." To assess stability, researchers need to subject black holes to minor disturbances and then see what happens to the solutions that describe these objects as time moves forward.
[....] 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. The final state conjecture depends on Kerr stability and on other sub-conjectures that are extremely challenging in themselves. "We have absolutely no idea how to prove this," Giorgi admitted. To some, that statement might sound pessimistic. 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.
I can't imagine being asked to peer review a 912-page mathematics paper that builds upon an 800-page paper. Take a stab at it yourself, if you've got a few weeks to spare.
(Score: 2, Interesting) by Anonymous Coward on Wednesday August 24 2022, @11:22AM (3 children)
1. At first glance the text is not very dense.
2. It's not pure mathematics, there are constraints on boundary ("initial") conditions, which means it's more "physics", since it discusses "real/realistic" universes.
3. I'm not a specialist, so I don't know how well-established the notations are, and this will influence the ease of reviewing.
4. I don't know what it means to review such a paper: for physics, in particular experiments, the task is to ensure that the results are "reproducible", in the sense that someone who reads the paper can repeat the experiment (but the reviewer's task is NOT to repeat the experiment). Are mathematicians supposed to confirm every step of the proof is correct? Or are they supposed to confirm that others can follow the proof to confirm it is correct?
(Score: 3, Interesting) by PiMuNu on Wednesday August 24 2022, @04:10PM (1 child)
My understanding is that mathematics papers are expected to be reviewed to validate the proof i.e.
> Are mathematicians supposed to confirm every step of the proof is correct?
Yes. They often find mistakes (naturally, as 900 page proof is likely to have errors).
(Score: 2) by legont on Wednesday August 24 2022, @11:33PM
It's pretty much guaranteed that there are math "issues". After all physics does not follow strict math.
It does not mean it is wrong though.
What they did is likely they found a solution of certain equations under certain border conditions which may or may be not reasonable.
"Wealth is the relentless enemy of understanding" - John Kenneth Galbraith.
(Score: 3, Informative) by bzipitidoo on Wednesday August 24 2022, @05:48PM
What I wonder is, how is such a long paper published? What journals take such long papers? Many journals are pretty rigid about limiting submissions to 10 pages. Some have "special" categories that allow up to 25 pages. But so far as I know, none come anywhere near allowing a 900 page submission. Of course, things have been changing pretty fast, and yet, not as fast as they could have. Academic publishing has had to be dragged kicking and screaming into the Information Age. Some of the biggest reasons for the 10 page limit was simple lack of space in the printed medium. But we no longer have to limit ourselves to what print can do.
For something big like this, it looks like the scientists simply bypass the journals. Good! Post the monstrosity on Arxiv. Alert those among their colleagues they know will be interested. Need to have a pretty good reputation for that work.
(Score: 2) by cosurgi on Wednesday August 24 2022, @05:49PM
This highlights how much we are lacking in the field of automatic proof checking. There are some tools for that, like coq [1] proof assistant. But we are far from the state where you could just feed a proof into a proof compiler and check if it "compiles" without an error. Plenty of work ahead of us.
[1] https://coq.inria.fr/ [inria.fr]
#
#\ @ ? [adom.de] Colonize Mars [kozicki.pl]
#