Black hole stability conjecture
The black hole stability conjecture is the conjecture that a perturbed Kerr black hole will settled back down to a stable state. This has been an open problem in general relativity for some time. A 2016 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 et. al. in 2017. Culminating in 2022, a series of papers was published by Klainerman et. al. which present a proof of the conjecture for slowly rotating Kerr black holes in Minkowski space-time. See also 
 Final state conjecture

References 

Black holes
General relativity
Conjectures that have been proved