## Columbia Mathematics Department Colloquium

# On the rigidity of black holes*
*

by

# Sergiu Klainerman

## Princeton University

Abstract:

The classical result on the uniqueness of black
holes in GR, due to Hawking, which asserts that regular, stationary
solutions of the Einstein vacuum equations must be isometric to an
admissible black hole Kerr solution, has at its core a a highly
unrealistic analyticity assumption for the metric.

The goal of the talk is to survey recent results, obtained in
collaboration with Alexakis and Ionescu, on the general rigidity
problem, without analyticity.