Stable black holes: in vacuum and beyond

Author:

Giorgi Elena

Abstract

Black holes are important objects in our understanding of the universe, as they represent the extreme nature of General Relativity. The mathematics behind them has surprising geometric properties, and their dynamics is governed by hyperbolic partial differential equations. A basic question one may ask is whether these solutions to the Einstein equation are stable under small perturbations, which is a typical requirement to be physically meaningful. We illustrate the main conjectures regarding the stability problem of known black hole solutions and present some recent theorems regarding the fully nonlinear evolution of black holes in the case of vacuum and their interaction with matter fields.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

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1. Corrigendum to “Stable black holes: In vacuum and beyond”;Bulletin of the American Mathematical Society;2023-04-03

2. Mathematical model for Sagittarius A* and related Tolman–Oppenheimer–Volkoff equations;Mathematical Methods in the Applied Sciences;2023-03-05

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