Self-forces from generalized Killing fields

TL;DR

This paper develops a non-perturbative geometric formalism to analyze self-forces on extended scalar charges in curved spacetimes, simplifying motion laws and clarifying self-interaction effects.

Contribution

It introduces a new geometric framework using generalized Killing fields to derive laws of motion and interpret self-interactions in curved spacetime.

Findings

Simplifies understanding of self-forces and self-torques.

Provides a geometric interpretation of self-interactions.

Recovers standard results for small charge distributions.

Abstract

A non-perturbative formalism is developed that simplifies the understanding of self-forces and self-torques acting on extended scalar charges in curved spacetimes. Laws of motion are locally derived using momenta generated by a set of generalized Killing fields. Self-interactions that may be interpreted as arising from the details of a body's internal structure are shown to have very simple geometric and physical interpretations. Certain modifications to the usual definition for a center-of-mass are identified that significantly simplify the motions of charges with strong self-fields. A derivation is also provided for a generalized form of the Detweiler-Whiting axiom that pointlike charges should react only to the so-called regular component of their self-field. Standard results are shown to be recovered for sufficiently small charge distributions.