The singular field used to calculate the self-force on non-spinning and spinning particles

TL;DR

This paper introduces a method to compute the singular field for particles in curved spacetime, aiding in self-force calculations for scalar, electromagnetic, and gravitational fields, with practical expansion catalogs for geodesic motion.

Contribution

It provides a novel approach and detailed expansions for the singular field associated with monopole and dipole sources in curved spacetime, enhancing self-force computations.

Findings

Catalog of singular field expansions for various fields

Method for calculating the singular field using a new Green's function

Facilitates self-force analysis for particles in curved spacetime

Abstract

The singular field of a point charge has recently been described in terms of a new Green's function of curved spacetime. This singular field plays an important role in the calculation of the self-force acting upon the particle. We provide a method for calculating the singular field and a catalog of expansions of the singular field associated with the geodesic motion of monopole and dipole sources for scalar, electromagnetic and gravitational fields. These results can be used, for example, to calculate the effects of the self-force acting on a particle as it moves through spacetime.