Overdamped modes in Schwarzschild-de Sitter and a Mathematica package for the numerical computation of quasinormal modes

TL;DR

This paper introduces a Mathematica package that simplifies the numerical computation of quasinormal modes for various black hole spacetimes, enabling efficient analysis across different asymptotic geometries.

Contribution

The paper presents a versatile Mathematica tool for computing quasinormal modes, applicable to diverse black hole backgrounds, with detailed tutorials and a review of the underlying method.

Findings

Identified a new infinite set of purely imaginary modes in Schwarzschild-de Sitter black holes.

Successfully computed QNMs for Reissner-Nordström black branes in anti-de Sitter space.

Demonstrated the method's applicability to multiple spacetime asymptotics.

Abstract

We present a package for Mathematica that facilitates the numerical computation of the quasinormal mode (QNM) spectrum of a black hole/black brane. Requiring as input only the QNM equation(s), the application of a single Mathematica function will compute the spectrum efficiently, by discretizing the equation(s) and solving the resulting generalized eigenvalue equation. It is applicable to a large variety of black holes, independent of their asymptotics. The package comes fully documented and with several tutorials. Here we present a self-contained review of the method and consider several applications. We illustrate the method in the simplest case of scalar QNMs of a Schwarzschild black brane in anti-de Sitter. Then we go on to look at the scalar QNMs of the Schwarzschild black hole in de Sitter, in anti-de Sitter and in asymptotically flat spacetimes, finding a novel infinite set of purely imaginary modes in the first case. We also derive the QNM equations for a generic Einstein-Maxwell-scalar background and use these to compute the QNMs of the asymptotically anti-de Sitter Reissner-Nordstr\"{o}m black brane, as a further illustration and check of the method.