Scalar field and electromagnetic perturbations on Locally Rotationally Symmetric spacetimes

TL;DR

This paper develops a covariant, gauge-invariant formalism to analyze scalar and electromagnetic perturbations in LRS class II spacetimes, deriving generalized wave equations and applying them to Schwarzschild, Vaidya, and dust universe models.

Contribution

It introduces a new covariant, gauge-invariant approach to perturbations in LRS class II spacetimes, deriving generalized Regge-Wheeler equations for these perturbations.

Findings

Derived covariant wave equations for scalar and electromagnetic perturbations.

Applied the formalism to Schwarzschild, Vaidya, and dust universe spacetimes.

Provided detailed analysis and discussion of perturbations in these models.

Abstract

We study scalar field and electromagnetic perturbations on Locally Rotationally Symmetric (LRS) class II spacetimes, exploiting a recently developed covariant and gauge-invariant perturbation formalism. From the Klein-Gordon equation and Maxwell's equations, respectively, we derive covariant and gauge-invariant wave equations for the perturbation variables and thereby find the generalised Regge-Wheeler equations for these LRS class II spacetime perturbations. As illustrative examples, the results are discussed in detail for the Schwarzschild and Vaidya spacetime, and briefly for some classes of dust Universes.