Extended-body approach to the electromagnetic self-force in curved spacetime

TL;DR

This paper derives the electromagnetic self-force on a charged particle in curved spacetime using a novel extended-body approach, modeling the particle as a dumbbell of two charges and carefully handling divergences through mass renormalization.

Contribution

It generalizes the extended-body approach to curved spacetime, providing a new derivation of the electromagnetic self-force for arbitrary curved backgrounds.

Findings

Successfully derives the standard self-force expression in curved spacetime.

Shows divergences can be removed via mass renormalization.

Extends flat spacetime methods to curved spacetime context.

Abstract

We offer a novel derivation of the electromagnetic self-force acting on a charged particle moving in an arbitrary curved spacetime. Our derivation is based on a generalization from flat spacetime to curved spacetime of the extended-body approach of Ori and Rosenthal. In this approach the charged particle is first modeled as a body of finite extension s, the net force acting on the extended body is computed, and the limit s -> 0 is taken at the end of the calculation. Concretely our extended body is a dumbbell that consists of two point charges that are maintained at a constant spacelike separation s. The net force acting on the dumbbell includes contributions from the mutual forces exerted on each charge by the field created by the other charge, the individual self-forces exerted on each charge by its own field, and the external force which is mostly responsible for the dumbbell's acceleration. These contributions are added up, in a way that respects the curved nature of the spacetime, and all diverging terms in the net force are shown to be removable by mass renormalization. Our end result, in the limit s -> 0, is the standard expression for the electromagnetic self-force in curved spacetime.