# 2016-2017 Chern Lectures

**The 2016-2017 Chern Lectures** were given by Sergiu Klainerman of Princeton University, on January 31 and February 1, 2 and 3, 2017. The title of the series was "On the Mathematical Theory of Black Holes".

**On the Mathematical Theory of Black Holes**

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

**Lecture 1:**

Tuesday, January 31, 2017

4:00 pm - 5:00 pm, Banatao Auditorium, 310 Sutardja Dai Hall

On the reality of black holes

Abstract: I will give a quick introduction to the initial value problem in general relativity, along with an overview of the problems of rigidity, stability and collapse, and how they fit with regard to the Final State Conjecture.

*A reception in honor of the speaker will be held following the first lecture at 5:15 pm in 1015 Evans Hall.*

**Lecture 2:**

Wednesday, February 1, 2017

4:00 pm - 5:00 pm, Banatao Auditorium, 310 Sutardja Dai Hall

Rigidity of black holes

**Lecture 3:**

Thursday, February 2, 2017

4:00 pm - 5:00 pm, Room 60, Evans Hall

The problem of stability

**Lecture 4:**

Friday, February 3, 2017

4:00 pm - 5:00 pm, Room 939, Evans Hall

The problem of collapse