Quasinormal modes of small Schwarzschild-de Sitter black holes

TL;DR

This paper investigates how quasinormal modes of Schwarzschild-de Sitter black holes behave as the black hole mass approaches zero, showing convergence to de Sitter space modes with supporting numerical evidence.

Contribution

It provides a rigorous analysis of the limiting behavior of QNMs for small black holes and introduces uniform estimates for related ODEs.

Findings

QNMs converge to de Sitter modes as black hole mass tends to zero

Uniform estimates for a family of degenerating ODEs are established

Numerical simulations support the theoretical results

Abstract

We study the behavior of the quasinormal modes (QNMs) of massless and massive linear waves on Schwarzschild-de Sitter black holes as the black hole mass tends to 0. Via uniform estimates for a degenerating family of ODEs, we show that in bounded subsets of the complex plane and for fixed angular momenta, the QNMs converge to those of the static model of de Sitter space. Detailed numerics illustrate our results and suggest a number of open problems.