Current Developments in Mathematics

Volume 2020

The black hole stability problem

Pages: 105 – 155



Andras Vasy (Department of Mathematics, Stanford University, Stanford, California, U.S.A.)


These lectures concern the stability of black holes, which are certain Lorentzian manifolds solving Einstein’s equation—the first lecture will mostly discuss what these black holes are and what stability means. These notes follow the general structure of the actual lectures, with Sections 1–5 comprising the first lecture, while the rest covers the second, more technical, lecture as well as various extensions.

These lecture notes are based on joint work with Peter Hintz, and in part with Dietrich Häfner. The author gratefully acknowledges support from the National Science Foundation under grant number DMS-1953987.

Published 30 September 2022