A characteristic approach to the quasi-normal mode problem

Abstract

In this paper we discuss a new approach to the quasinormal-mode problem in general relativity. By combining a characteristic formulation of the perturbation equations with the integration of a suitable phase-function for a complex valued radial coordinate, we reformulate the standard outgoing-wave boundary condition as a zero Dirichlet condition. This has a number of important advantages over previous strategies. The characteristic formulation permits coordinate compactification, which means that we can impose the boundary condition at future null infinity. The phase function avoids oscillatory behaviour in the solution, and the use of a complex radial variable allows a clean distinction between out- and ingoing waves. We demonstrate that the method is easy to implement, and that it leads to high precision numerical results. Finally, we argue that the method should generalise to the important problem of rapidly rotating neutron star spacetimes.

14 pages, 3 figures, 3 tables. v2: Minor revisions, matches published version

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• Axial quasi-normal modes of neutron stars: Accounting for the superfluid in the crust
• A new approach to the study of quasi-normal modes of rotating stars
• Non-axisymmetric oscillations of differentially rotating relativistic stars
• Quasinormal Modes in Modified Gravity using Physics-Informed Neural Networks
• Multi-messenger Emission from Tidal Waves in Neutron Star Oceans
• Quasinormal modes of a Schwarzschild black hole within the Bondi-Sachs framework
• Perturbation theory of spherically symmetric self-similar black holes
• Axial Quasi-normal modes of Neutron Stars with Exotic Matter