[Paper Review] Extended-body approach to the electromagnetic self-force in curved spacetime

Javier Molina Sánchez, Eric Poisson|ArXiv.org|Dec 20, 2005

Experimental and Theoretical Physics Studies2 references3 citations

TL;DR

This paper presents a novel derivation of the electromagnetic self-force in curved spacetime using an extended-body approach, modeling a charged particle as a dumbbell of two point charges separated by a finite distance s. By computing the net force on the dumbbell and taking the limit s→0, the authors recover the standard expression for the self-force, demonstrating consistency despite limitations in modeling internal dynamics.

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.

Motivation & Objective

• To provide an alternative derivation of the electromagnetic self-force in curved spacetime using an extended-body framework.
• To address the limitations of existing derivations, which are considered unsatisfactory due to conceptual or technical flaws.
• To explore whether a consistent extended-body model can yield the standard self-force expression without relying on axiomatic assumptions about the singular field.
• To assess the robustness of force addition in curved spacetime under different parallel transport rules.
• To motivate future work toward a fully physical model of extended charge distributions with realistic internal dynamics.

Proposed method

• Model the charged particle as a dumbbell composed of two point charges separated by a fixed spacelike distance s in curved spacetime.
• Compute the net force on the dumbbell, including mutual electromagnetic forces, individual self-forces, and external forces.
• Use Fermi normal coordinates to systematically handle the curved spacetime geometry and define local inertial frames along the worldline.
• Apply the Ori-Rosenthal prescription to transport individual forces to a common point for summation, generalizing it to curved spacetime.
• Identify and remove divergent terms via mass renormalization, showing they are removable in the s→0 limit.
• Take the limit s→0 to recover the standard expression for the electromagnetic self-force, confirming consistency with known results.

Experimental results

Research questions

• RQ1 Can the electromagnetic self-force in curved spacetime be consistently derived using an extended-body model with finite charge separation?
• RQ2 How sensitive is the final self-force result to the choice of parallel transport rule used to combine forces at different points?
• RQ3 What role do individual self-forces on each point charge play in the overall force balance of the extended body?
• RQ4 To what extent can divergences in the force calculation be removed through mass renormalization in curved spacetime?
• RQ5 Is the extended-body approach capable of yielding the standard self-force expression without relying on axiomatic assumptions about the singular field?

Key findings

• The extended-body approach successfully reproduces the standard expression for the electromagnetic self-force in curved spacetime in the limit s→0.
• Divergent terms arising in the force calculation are removable via mass renormalization, confirming consistency with effective field theory principles.
• The final self-force is largely insensitive to the specific details of the parallel transport rule used to combine forces at different points along the worldline.
• Each point charge within the dumbbell must be assigned its own self-force, which is essential for consistency and cannot be neglected in the derivation.
• The use of Fermi normal coordinates provides a natural and effective framework for handling curved spacetime effects in the derivation.
• The derivation highlights the need for a more physically realistic internal model of extended charges, as the current dumbbell model is artificial and lacks a description of cohesive forces.