Axial perturbations of general spherically symmetric spacetimes
Abstract
The aim of this paper is to present a governing equation for first order axial metric perturbations of general, not necessarily static, spherically symmetric spacetimes. Under the non-restrictive assumption of axisymmetric perturbations, the governing equation is shown to be a two-dimensional wave equation where the wave function serves as a twist potential for the axisymmetry generating Killing vector. This wave equation can be written in a form which is formally a very simple generalization of the Regge-Wheeler equation governing the axial perturbations of a Schwarzschild black hole, but in general the equation is accompanied by a source term related to matter perturbations. The case of a viscous fluid is studied in particular detail.
Cite
@article{arxiv.gr-qc/0111066,
title = {Axial perturbations of general spherically symmetric spacetimes},
author = {Max Karlovini},
journal= {arXiv preprint arXiv:gr-qc/0111066},
year = {2010}
}
Comments
16 pages, no figures, minor corrections