The black hole stability conjecture is the conjecture that a perturbed Kerr black hole in Minkowski space will settle back down to a stable state. The question developed out of work in 1952 by the French mathematician Yvonne Choquet-Bruhat.
The stability of empty Minkowski space is a result of Klainerman and Christodoulou from 1993.
A 2016 by Hintz and Vasy paper proved the stability of slowly rotating Kerr black holes in de Sitter space.
A limited stability result for Kerr black holes in Schwarzschild space-time was published by Klainerman and Szeftel in 2017.
Culminating in 2022, a series of papers was published by Giorgi, Klainerman and Szeftel which present a proof of the conjecture for slowly rotating Kerr black holes in Minkowski space-time.