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

• Published in: European physical journal plus Vol. 132; no. 12; p. 546
• Main Author: Jansen, Aron
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.12.2017; Springer Nature B.V
• Subjects: Applied and Technical Physics; Asymptotic properties; Atomic; Black holes; Branes; Complex Systems; Computation; Condensed Matter Physics; Eigenvalues; Equilibrium; Fluid mechanics; Gravitational waves; Gravity; Mathematical and Computational Physics; Molecular; Numerical analysis; Optical and Plasma Physics; Ordinary differential equations; Physics; Physics and Astronomy; Spacetime; Theoretical; Theory of relativity
• ISSN: 2190-5444; 2190-5444
• DOI: 10.1140/epjp/i2017-11825-9

. 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, independently 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-Nordström black brane, as a further illustration and check of the method.