Nonoscillatory gravitational quasinormal modes and telling tails for Schwarzschild-de Sitter black holes

TL;DR

This paper uncovers a new branch of purely imaginary gravitational quasinormal modes in Schwarzschild-de Sitter black holes, linking them to exponential tails and revealing their behavior as the cosmological constant varies.

Contribution

It identifies a novel branch of purely imaginary modes in the quasinormal spectrum and analyzes their relation to exponential tails and the limits of de Sitter spacetime.

Findings

New purely imaginary modes form a distinct branch in the spectrum.

These modes contribute to exponential asymptotic tails.

Modes approach de Sitter spacetime behavior as horizon ratio vanishes.

Abstract

We show that the quasinormal spectrum of gravitational perturbations of Schwarzschild - de Sitter black holes contains a new branch of purely imaginary modes. These modes are not algebraically special and we showed that the sum of them form the well-known in the literature exponential asymptotic tail. When the ratio of the event horizon radius to the cosmological horizon vanishes, these quasinormal modes approach modes of empty de Sitter spacetime. Thus, the spectrum consists of the two branches: Schwarzschild branch deformed by the cosmological constant and de Sitter branch deformed by the black hole mass. While the de Sitter branch contains purely imaginary modes only, the oscillatory modes (with nonzero real part) of the Schwarzschild branch can also become purely imaginary for some values of the cosmological constant, for which they approach the algebraically special mode.