Electromagnetic self-forces and generalized Killing fields

TL;DR

This paper develops a formalism using generalized Killing fields to analyze electromagnetic self-forces on extended charges in curved spacetime, deriving exact and approximate equations for their motion, including effects like dipole and spin forces.

Contribution

It introduces a new formalism with generalized Killing fields to understand self-forces and derives exact and approximate equations of motion for extended charges in curved spacetime.

Findings

Derived exact evolution equations for effective momenta.

Showed a modified Detweiler-Whiting axiom simplifies self-force analysis.

Included dipole and spin forces in equations of motion.

Abstract

Building upon previous results in scalar field theory, a formalism is developed that uses generalized Killing fields to understand the behavior of extended charges interacting with their own electromagnetic fields. New notions of effective linear and angular momenta are identified, and their evolution equations are derived exactly in arbitrary (but fixed) curved spacetimes. A slightly modified form of the Detweiler-Whiting axiom that a charge's motion should only be influenced by the so-called "regular" component of its self-field is shown to follow very easily. It is exact in some interesting cases, and approximate in most others. Explicit equations describing the center-of-mass motion, spin angular momentum, and changes in mass of a small charge are also derived in a particular limit. The chosen approximations -- although standard -- incorporate dipole and spin forces that do not appear in the traditional Abraham-Lorentz-Dirac or Dewitt-Brehme equations. They have, however, been previously identified in the test body limit.