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

TL;DR

This paper proposes an axiomatic framework to derive electromagnetic and gravitational self-forces (radiation reaction) for small bodies in curved spacetime, using a comparison axiom that regularizes the point-particle limit by examining differences between similarly composed bodies. The electromagnetic analysis yields a self-force comprising the incoming field, an Abraham–Lorentz–type damping term, a local curvature term, and a tail integral, with a reduced-order equation that resolves runaway behavior. The gravitational analysis mirrors the electromagnetic approach, producing a tail-dominated self-force term after reduction of order, in agreement with prior results by Mino et al. The tail term is the essential nonlocal contribution, and the framework provides a conceptually simpler route to known results while highlighting gauge considerations and the need for rigorous justification of the axioms.

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.