Mathematics Department Colloquium: Stability of black holes

Colloquium | April 20 | 4:10-5 p.m. | 60 Evans Hall

 Peter Hintz, UC Berkeley

 Department of Mathematics

More than a hundred years ago, Schwarzschild first wrote down the mathematical description of a black hole; on a technical level, black holes are certain types of solutions of Einstein's equations of general relativity. While they have since become part of popular culture, many fundamental questions about them remain unanswered: for example, it is not yet known mathematically if they are stable! I will explain what that means and outline a recent proof of full nonlinear stability (obtained in joint work with A. Vasy) under the condition that the cosmological constant is positive, an assumption consistent with current cosmological models. The talk is intended as a non-technical introduction to the subject, with a focus on the central role played by modern microlocal and spectral theoretical techniques.