The Motion of Small Bodies in Space-time

TL;DR

This paper rigorously analyzes the motion of small bodies in general relativity, showing they follow geodesics or Lorentz-force curves, and clarifies the connection between different modeling approaches, including wave packet fields.

Contribution

It provides a precise mathematical formulation of small body motion in general relativity, bridging distributional and smooth field models, and extends to wave packet fields.

Findings

Small bodies follow geodesics or Lorentz-force curves.

Clarifies the relationship between distributional and smooth models.

Formulates the optical limit for Maxwell fields.

Abstract

We consider the motion of small bodies in general relativity. The key result captures a sense in which such bodies follow timelike geodesics (or, in the case of charged bodies, Lorentz-force curves). This result clarifies the relationship between approaches that model such bodies as distributions supported on a curve, and those that employ smooth fields supported in small neighborhoods of a curve. This result also applies to "bodies" constructed from wave packets of Maxwell or Klein-Gordon fields. There follows a simple and precise formulation of the optical limit for Maxwell fields.