Scalar, electromagnetic, and gravitational self-forces in weakly curved spacetimes

TL;DR

This paper computes scalar, electromagnetic, and gravitational self-forces in weakly curved spacetimes, revealing both conservative and radiation-reaction components, with surprising implications for gravitational self-force and radiation damping.

Contribution

It provides a detailed calculation of self-forces in weakly curved spacetimes, highlighting the distinction between matter-dependent conservative parts and matter-insensitive radiation-reaction parts.

Findings

Self-force contains conservative and radiation-reaction parts.

Conservative self-force relates to matter presence.

Radiation-reaction force appears unexpectedly in gravity case.

Abstract

We calculate the self-force experienced by a point scalar charge, a point electric charge, and a point mass moving in a weakly curved spacetime characterized by a time-independent Newtonian potential. The self-forces are calculated by first computing the retarded Green's functions for scalar, electromagnetic, and (linearized) gravitational fields in the weakly curved spacetime, and then evaluating an integral over the particle's past world line. In all three cases the self-force contains both a conservative and a nonconservative (radiation-reaction) part. The conservative part of the self-force is directly related to the presence of matter in the spacetime. The radiation-reaction part of the self-force, on the other hand, is insensitive to the presence of matter. Our result for the gravitational self-force is disturbing: a radiation-reaction force should not appear in the equations of motion at this level of approximation, and it should certainly not give rise to radiation antidamping. The last section of this paper attempts to make sense of this result by placing it in the context of the post-Newtonian N-body problem.