Axiomatic approach to radiation reaction of scalar point particles in curved spacetime

TL;DR

This paper develops an axiomatic framework to derive a general expression for the self-force on a scalar point particle moving in curved spacetime, aiding understanding of radiation reaction effects in gravitational physics.

Contribution

It generalizes Quinn and Wald's axiomatic approach to include arbitrary trajectories, providing a comprehensive formula for scalar self-force in curved backgrounds.

Findings

Derived a general self-force expression for scalar particles in curved spacetime.

Explored equations of motion considering radiation reaction effects.

Provides a foundation for analyzing particle dynamics in gravitational wave contexts.

Abstract

Several different methods have recently been proposed for calculating the motion of a point particle coupled to a linearized gravitational field on a curved background. These proposals are motivated by the hope that the point particle system will accurately model certain astrophysical systems which are promising candidates for observation by the new generation of gravitational wave detectors. Because of its mathematical simplicity, the analogous system consisting of a point particle coupled to a scalar field provides a useful context in which to investigate these proposed methods. In this paper, we generalize the axiomatic approach of Quinn and Wald in order to produce a general expression for the self force on a point particle coupled to a scalar field following an arbitrary trajectory on a curved background. Our equation includes the leading order effects of the particle's own fields, commonly referred to as ``self force'' or ``radiation reaction'' effects. We then explore the equations of motion which follow from this expression in the absence of non-scalar forces.