Effects of the singular self-field on the motion of an extended body

TL;DR

This paper introduces a formalism that simplifies calculating self-forces on extended bodies in curved spacetime, showing that the dominant self-field component effectively renormalizes the body's multipole moments.

Contribution

It presents a new formalism that clarifies the role of the self-field in the motion of extended bodies, emphasizing the renormalization of multipole moments.

Findings

The regular part of the self-field dominates the self-force effects.

The remaining self-field component acts to renormalize multipole moments.

The formalism applies to scalar, electromagnetic, and gravitational cases.

Abstract

A formalism is described that greatly simplifies the derivation of scalar, electromagnetic, and gravitational self-forces and self-torques acting on extended bodies in curved spacetimes. Commonly-studied aspects of these effects are normally dominated by the so-called "regular" component of a body's self-field. The only consequence of the remaining (much larger) portion of the self-field turns out to be very simple. It exerts forces and torques that effectively renormalize all multipole moments of the body's stress-energy tensor in its laws of motion.