A characteristic approach to the quasi-normal mode problem

Details A characteristic approach to the quasi-normal mode problem A characteristic approach to the quasi-normal mode problem

2007-05-31

arxiv.org/abs/0705.4585v2

Class.Quant.Grav.24:4147-4160,2007

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

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

Scientific paper

10.1088/0264-9381/24/16/010

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.

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