Gravitational self force and gauge transformations

TL;DR

This paper investigates how the gravitational self force on a particle in curved spacetime changes under gauge transformations, extending regularization methods to arbitrary gauges and analyzing gauge regularity issues.

Contribution

It derives a general gauge transformation law for the self force, extends regularization and mode-sum methods to arbitrary gauges, and analyzes gauge regularity in Schwarzschild spacetime.

Findings

Gauge transformation law for the self force derived.

Regularization parameters are gauge-independent.

Transformation to the radiation gauge is irregular for all orbits.

Abstract

We explore how the gravitational self force (or ``radiation reaction'' force), acting on a pointlike test particle in curved spacetime, is modified in a gauge transformation. We derive the general transformation law, describing the change in the self force in terms of the infinitesimal displacement vector associated with the gauge transformation. Based on this transformation law, we extend the regularization prescription by Mino et al. and Quinn and Wald (originally formulated within the harmonic gauge) to an arbitrary gauge. Then we extend the method of mode-sum regularization (which provides a practical means for calculating the regularized self force and was recently applied to the harmonic-gauge gravitational self force) to an arbitrary gauge. We find that the regularization parameters involved in this method are gauge-independent. We also explore the gauge transformation of the self force from the harmonic gauge to the Regge-Wheeler gauge and to the radiation gauge, focusing attention on the regularity of these gauge transformations. We conclude that the transformation of the self force to the Regge-Wheeler gauge in Schwarzschild spacetime is regular for radial orbits and irregular otherwise, whereas the transformation to the radiation gauge is irregular for all orbits.