Non-linear relativistic perturbation theory with two parameters

TL;DR

This paper develops a formalism for non-linear relativistic perturbation theory using two parameters, addressing gauge dependence and transformation rules, with applications to rotating stars.

Contribution

It introduces a two-parameter perturbative framework in relativistic theory and derives explicit higher-order gauge transformation rules.

Findings

Analysis of gauge dependence in two-parameter perturbations

Explicit higher-order gauge transformation formulas

Application to rotating star models

Abstract

An underlying fundamental assumption in relativistic perturbation theory is the existence of a parametric family of spacetimes that can be Taylor expanded around a background. Since the choice of the latter is crucial, sometimes it is convenient to have a perturbative formalism based on two (or more) parameters. A good example is the study of rotating stars, where generic perturbations are constructed on top of an axisymmetric configuration built by using the slow rotation approximation. Here, we discuss the gauge dependence of non-linear perturbations depending on two parameters and how to derive explicit higher order gauge transformation rules.