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.
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