A covariant approach for perturbations of rotationally symmetric spacetimes

TL;DR

This paper introduces a covariant, gauge-invariant method for analyzing perturbations in spherically symmetric and locally rotationally symmetric spacetimes, applicable to stellar and cosmological models.

Contribution

It develops a semi-tetrad, 1+1+2 covariant decomposition of Einstein's equations tailored for perturbations of symmetric spacetimes, enhancing analysis tools in cosmology and astrophysics.

Findings

Provides a covariant, gauge-invariant framework for perturbations.

Applicable to a range of models including stellar objects and cosmological solutions.

Facilitates analysis of perturbations in symmetric spacetimes.

Abstract

We present a covariant decomposition of Einstein's Field Equations which is particularly suitable for perturbations of spherically symmetric -- and general locally rotationally symmetric -- spacetimes. Based upon the utility of the 1+3 covariant approach to perturbation theory in cosmology, the semi-tetrad, 1+1+2 approach presented here should be useful for analysing perturbations of a variety of systems in a covariant and gauge-invariant manner. Such applications range from stellar objects to cosmological models such as the spherically symmetric Lemaitre-Tolman-Bondi solutions or the class of locally rotationally symmetric Bianchi models.