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A characteristic approach to the quasi-normal mode problem

A characteristic approach to the quasi-normal mode problem
A characteristic approach to the quasi-normal mode problem
In this paper we discuss a new approach to the quasi-normal 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 generalize to the important problem of rapidly rotating neutron star spacetimes.
0264-9381
4147-4160
Samuelsson, Lars
ce25b720-ee5b-4b1a-af84-c38a41399a62
Andersson, Nils
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Maniopoulou, Asimina
ada812b5-349a-4070-813d-6c535fa86c09
Samuelsson, Lars
ce25b720-ee5b-4b1a-af84-c38a41399a62
Andersson, Nils
2dd6d1ee-cefd-478a-b1ac-e6feedafe304
Maniopoulou, Asimina
ada812b5-349a-4070-813d-6c535fa86c09

Samuelsson, Lars, Andersson, Nils and Maniopoulou, Asimina (2007) A characteristic approach to the quasi-normal mode problem. Classical and Quantum Gravity, 24 (16), 4147-4160. (doi:10.1088/0264-9381/24/16/010).

Record type: Article

Abstract

In this paper we discuss a new approach to the quasi-normal 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 generalize to the important problem of rapidly rotating neutron star spacetimes.

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More information

Published date: 21 August 2007

Identifiers

Local EPrints ID: 48200
URI: http://eprints.soton.ac.uk/id/eprint/48200
ISSN: 0264-9381
PURE UUID: 4c2334b4-901a-4316-b80d-54884cd6323f
ORCID for Nils Andersson: ORCID iD orcid.org/0000-0001-8550-3843

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Date deposited: 04 Sep 2007
Last modified: 09 Jan 2022 02:57

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Contributors

Author: Lars Samuelsson
Author: Nils Andersson ORCID iD
Author: Asimina Maniopoulou

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