Calculating the self force in Schwarzschild spacetime by mode-sum regularization

TL;DR

This paper presents a mode-sum regularization method for calculating the self force on a scalar particle in Schwarzschild spacetime, including explicit results for static and circular orbits.

Contribution

It introduces a novel mode-sum regularization technique for self force calculations in Schwarzschild spacetime, with practical implementation details.

Findings

Successfully applied to static particles

Extended to uniform circular motion

Provides explicit computational results

Abstract

We outline a method for calculating the self force (the "radiation reaction force") acting on a scalar particle in a strong field orbit in a Schwarzschild spacetime. In this method, the contribution to the self force associated with each multipole mode of the particle's field is calculated separately, and the sum over modes is then evaluated, subject to a certain regularization procedure. We present some explicit results concerning the implementation of the calculation scheme for a static particle, and also for a uniform circular motion, on the Schwarzschild background.