Quasinormal modes of small Schwarzschild–de Sitter black holes

We study the behavior of 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 ordinary differential equations, 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.