Seminar| Institute of Mathematical Sciences
Time: Tuesday, Feburary 25th, 2025,16:00-17:00
Location: IMS, RS408
Speaker:Allen Juntao Fang, University of Muenster
Abstract:Black hole stability is a central topic in mathematical relativity that has seen numerous advancements in recent years. Both the Kerr-de Sitter and the Kerr black hole spacetimes have been proven to be stable in the slowly-rotating regime. However, the methods used have been markedly different, as well as the decay rates proven. Perturbations of Kerr-de Sitter converge exponentially back to a nearby Kerr-de Sitter black hole, while perturbations of Kerr only converge polynomially back to the family. In this talk, I will introduce some basic ideas in analyzing wave behavior on black hole spacetimes and speak about wave behavior that is uniform in the cosmological constant by considering solutions to the model Regge-Wheeler equations in Kerr(-de Sitter). The main point is a careful handling of the relevant estimates on the region of the spacetime far from the black hole. This provides a first step into understanding the uniform (in the cosmological constant) stability of black hole spacetimes. This is joint work with Jeremie Szeftel and Arthur Touati.