Self force from equivalent periodic sources

TL;DR

This paper introduces a method to compute the self-force and radiation for a small body orbiting a black hole by decomposing the source into equivalent periodic motions, simplifying calculations and regularization.

Contribution

It proposes a novel decomposition of aperiodic sources into equivalent periodic motions, reducing self-force calculations to solving PDEs and improving regularization techniques.

Findings

Self-force computation reduces to solving PDEs with periodic time.

Extended sources alleviate regularization issues.

Decomposition method applies to aperiodic orbits around black holes.

Abstract

Considering the self force and radiation due to a small body in orbit (especially aperiodic) around a black hole, this paper defines a decomposition of the source into a sum over the shape preserving periodic motions of extended objects defined here consisting of ensembles of freely falling point particles. The stationary component is found to be within the conservative sector. Self-force computation throughout a specified trajectory reduces to solving one spatial partial differential equation (PDE) and a series of PDE's with periodic time. Regularization is alleviated due to the sources' extended nature. A regularization method is suggested inspired by the type present in electrostatics with surface or other singular sources.