In 1973, Penrose conjectured a lower bound on the mass M of a black hole as a function of its area A:
M ≥ sqrt(A/16π)
This is called the Penrose inequality, and it's resisted proof for a long time, though in 2001 Huisken-Ilmanen and Bray proved a special case.
In December this year, Da Xu from China Mobile Research Institute came out with a paper that claims to prove the Penrose inequality. It's 449 pages long! I've only skimmed through it, and this sort of technical work on general relativity is not my field, so I have no opinion regarding its validity. I've heard claims that it was prepared with the help of AI.
Do any experts on the math of general relativity have an opinion?
arXiv.org
The Unconditional Spacetime Penrose Inequality
We prove the unconditional spacetime Penrose inequality for three-dimensional asymptotically flat initial data sets satisfying the dominant energy ...
