Gauge Invariant Perturbations of General Spherically Symmetric Spacetimes

TL;DR

This paper develops gauge-invariant variables and master equations for perturbations in general spherically symmetric spacetimes, enabling analytical calculations applicable to problems like the Effective-One-Body approach.

Contribution

It introduces a systematic method for constructing gauge-invariant variables and master equations in spherically symmetric spacetimes, including special cases for low angular momentum modes.

Findings

Derived gauge-invariant variables for perturbations

Formulated master equations for different gauges

Provided an example linking metric perturbations to source terms

Abstract

In this paper, the gauge choices in general spherically symmetric spacetimes have been explored. We construct the gauge invariant variables and the master equations for both the Detweiler easy gauge and the Regge-Wheeler gauge, respectively. The particular cases for $l=0,1$ are also been investigated. Our results provide analytical calculations of metric perturbation in general spherically symmetric spacetimes, which can be applied to various cases, including the Effective-One-Body problem. A simple example is presented to show how the metric perturbation components are related to the source perturbation terms.