The black hole stability problem

This is a short survey on the black hole stability problem written in honor of Yvonne Choquet Bruhat’s 100th birthday, subject very dear to her and to which she has contributed greatly, in particular her foundational local existence result [1] and the maximal globally hyperbolic development of a given initial data set. The main focus is on the recent results on the stability of slowly rotating Kerr contained in the sequence of works [2, 3, 4, 5, 6].