Stability Analysis of spherically symmetric space-time sourced by Anisotropic Fluids

Abstract

In this work, we analyze the stability of spherically symmetric spacetimes sourced by perfect and anisotropic uids under a class of gravitational per- turbations. This has been done in a gauge-invariant formalism developed by Ishibashi and Kodama, where the perturbation equations are written in terms of manifestly gauge-invariant variables. We study axial perturbations of such spacetimes. The perturbation equations reduce to a single master equation and the equations for conservation of the energy momentum tensor. As is well-known, axial perturbations do not excite the uid perturbations when the source is a perfect uid. We review this result and then show that when the uid is anisotropic, this is still true provided the vector de ning the di- rection of anisotropy is constant under the perturbation. Finally we conclude by taking a speci c example of a spacetime sourced by an anisotropic uid and analyzing the axial perturbations of this spacetime.