Chern Lectures: Lecture 4 : The problem of collapse

Lecture | February 3 | 4:10-5 p.m. | 939 Evans Hall

 Sergiu Klainerman, Princeton University

 Department of Mathematics

The gravitational waves detected recently by LIGO were produced in the final phase of the inward spiraling of two black holes before they collided to produce a more massive black hole. The experiment is entirely consistent with the so-called Final State Conjecture of general relativity, according to which general solutions of the initial value problem approach asymptotically, in any compact region, a Kerr black hole. Although the conjecture is so very easy to formulate and happens to be validated by both astrophysical observations as well as numerical experiments, it is far beyond our current mathematical understanding, let alone techniques. In fact, even the far simpler and fundamental question of the stability of the Kerr black hole remains wide open.

In my lectures I will address the issue of stability as well as other aspects of the mathematical theory of black holes, such as rigidity of black holes and the problem of collapse. The rigidity conjecture asserts that all stationary solutions of the Einstein vacuum equations must be Kerr black holes, while the problem of collapse addresses the issue of how black holes form in the first place from regular initial conditions. Recent advances on all these problems were made possible by a remarkable combination of novel geometric and analytic techniques, which I will try to outline in my lectures.