Perturbation theory and harmonic gauge propagation in general relativity, a particular example

TL;DR

This paper investigates how coordinate transformations within harmonic gauges influence analytical solutions of Einstein's equations, applying this understanding to stationary, axisymmetric solutions for rotating fluid sources.

Contribution

It provides an analysis of coordinate change effects on harmonic gauge solutions and applies this to a specific class of rotating fluid models in general relativity.

Findings

Coordinate transformations impact the form of analytical solutions in harmonic gauges.

Application to rotating fluid sources demonstrates practical implications.

Enhances understanding of gauge choices in Einstein's equations.

Abstract

We study how the changes of coordinates between the class of harmonic coordinates affect the analitycal solutions of Einstein's equations and we apply it to an analytical approach for stationary and axisymmetric solutions of Einstein equation used by the authors \cite{cmmr}, \cite{cugmmr} to solve the problem of a self-gravitating rigidly rotating perfect fluid compact source.