Are black holes stable? This question, which has played a central role in General Relativity ever since the discoveries of the Schwarzschild (1916) and Kerr (1963) solutions, can be formulated as a remarkably simple-to-state mathematical conjecture:
"Vacuum, asymptotically flat, initial data sets, sufficiently close to Kerr(a,m), |a|/m < 1, initial data, have maximal developments with complete future null infinity and with the domain of outer communication which approaches (globally) a nearby Kerr solution.”
In my talk I will review some of the most important contributions to this extremely rich subject and discuss the main ideas behind the recent resolution of the conjecture for slowly rotating Kerr solutions, that is when the ratio |a|/m is sufficiently small.
"The treatment of perturbations of Kerr spacetime has been prolixious in its complexity. Perhaps at a later time, the complexity will be unraveled by deeper insights. But meantime the analysis has led into a realm of the rococo, splendorous, joyful, and immensely ornate."