Black Hole Stability

Introduction

The discovery of black holes, first as explicit solutions of Einstein's equations of general relativity, and later as possible explanations of astrophysical phenomena, has revolutionized our understanding of the universe. From a mathematical perspective, a central issue is to investigate the stability of these fascinating objects. This is the focus of the present proposal containing the following work packages:

Work Packages

1. Kerr Stability Conjecture

This concerns the nonlinear stability of Kerr black holes, which form a 2-parameter family of explicit solutions to Einstein vacuum equations. It has become, since its discovery by R. Kerr in 1963, a central topic in general relativity, first during the golden age of black hole physics, and in the last twenty years in mathematical relativity.

These efforts have led to the recent resolution, by the PI and collaborators, of the conjecture in the slowly rotating case. The goal of this work package is to tackle the general case.

2. Black Hole Stability with Matter

The breakthrough concerning the stability of Kerr for Einstein vacuum equations opens the door to other physically relevant cases in the context of Einstein equations coupled to matter.

This work package aims at proving the stability of:

• Charged Kerr-Newman black holes for Einstein-Maxwell equations
• Kerr black holes for massless Einstein-Vlasov equations
• Kerr-de Sitter black holes in the case of an arbitrarily small cosmological constant

3. Price's Law and Kerr Stability

An open problem concerns the optimal decay rate for perturbations of Kerr that can be achieved in the Kerr stability problem. The analogous problem for corresponding linear toy models is known as Price's law.

Obtaining an optimal decay rate in the context of the Kerr stability problem would not only vastly extend Price's law, but it is also expected to have important implications on the Strong Cosmic Censorship conjecture concerning the deterministic character of Einstein equations.