An axiomatic approach to electromagnetic and gravitational radiation reaction of particles in curved spacetime

TL;DR

This paper develops an axiomatic framework to derive electromagnetic and gravitational self-force expressions for particles in curved spacetime, aligning with known results and emphasizing the conceptual understanding of point particles as idealizations.

Contribution

It introduces a comparison axiom to derive self-force formulas, providing a unified axiomatic approach for electromagnetic and gravitational cases in curved spacetime.

Findings

Electromagnetic self-force matches DeWitt-Brehme-Hobbs expression.

Gravitational self-force involves a tail term causing deviation from geodesics.

Supports the view that point particles are idealizations, not fundamental objects.

Abstract

The problem of determining the electromagnetic and gravitational ``self-force'' on a particle in a curved spacetime is investigated using an axiomatic approach. In the electromagnetic case, our key postulate is a ``comparison axiom'', which states that whenever two particles of the same charge $e$ have the same magnitude of acceleration, the difference in their self-force is given by the ordinary Lorentz force of the difference in their (suitably compared) electromagnetic fields. We thereby derive an expression for the electromagnetic self-force which agrees with that of DeWitt and Brehme as corrected by Hobbs. Despite several important differences, our analysis of the gravitational self-force proceeds in close parallel with the electromagnetic case. In the gravitational case, our final expression for the (reduced order) equations of motion shows that the deviation from geodesic motion arises entirely from a ``tail term'', in agreement with recent results of Mino et al. Throughout the paper, we take the view that ``point particles'' do not make sense as fundamental objects, but that ``point particle equations of motion'' do make sense as means of encoding information about the motion of an extended body in the limit where not only the size but also the charge and mass of the body go to zero at a suitable rate. Plausibility arguments for the validity of our comparison axiom are given by considering the limiting behavior of the self-force on extended bodies.