Adiabatic Expansion for Metric Perturbation and the condition to solve the Gauge Problem for Gravitational Radiation Reaction Problem

TL;DR

This paper develops a non-linear method using adiabatic approximation and a specific gauge condition to address the gauge problem in gravitational radiation reaction studies of relativistic two-body systems.

Contribution

It introduces a non-linear generalization of a black hole perturbation approach to effectively solve the gauge problem in gravitational radiation reaction analysis.

Findings

The method avoids the gauge problem under certain conditions.

It extends previous linear approaches to non-linear regimes.

Provides a framework for more accurate modeling of dissipative two-body systems.

Abstract

We examine the adiabatic approximation in the study of a relativistic two-body problem with the gravitational radiation reaction. We recently pointed out that the usual metric perturbation scheme using a perturbation of the stress-energy tensor may not be appropriate for study of the dissipative dynamics of the bodies due to the radiation reaction. We recently proposed a possible approach to solve this problem with a linear black hole perturbation. This paper proposes a non-linear generalization of that method for a general application of this problem. We show that, under a specific gauge condition, the method actually allows us to avoid the gauge problem.