Stability analysis of (a class of) anisotropic spacetimes

Abstract

We consider spherically symmetric spacetimes sourced by a fluid with pressure anisotropy in the radial direction. We use gauge-invariant perturbation theory to study the stability of this class of spacetimes under axial perturbations. We apply our results to three diverse examples. Two examples arise as endpoints of collapse of a ball of fluid --- one describes a well-behaved stellar interior and the other has a naked singularity. We prove the stability of the stellar interior both with respect to Dirichlet and quasinormal mode boundary conditions on the perturbation. Surprisingly, the naked singularity is also stable under axial perturbations. Lastly, we take the example of anisotropic cosmology to show that in this case, the relevant perturbations are those in which the direction of anisotropy is also perturbed.

25 pages, references added, version to appear in Phys. Rev. D

References in corpus (7)

• All static spherically symmetric anisotropic solutions of Einstein's equations
• How to tell a gravastar from a black hole
• Ergoregion instability of ultra-compact astrophysical objects
• On the ergoregion instability in rotating gravastars
• Towards the description of anisotropic plasma at strong coupling
• Anisotropic plasma with a chemical potential and scheme-independent instabilities
• Scalar Field Probes of Power-Law Space-Time Singularities