On the Equation of Motion for a Fast Moving Small Object in the Strong Field Point Particle Limit

TL;DR

This paper derives a divergence-free equation of motion for a small, fast-moving object in a strong gravitational field, generalizing geodesic motion for non-rotating spherical objects in arbitrary backgrounds.

Contribution

It provides a straightforward, divergence-free derivation of the equation of motion using the strong field point particle limit, extending previous results.

Findings

Equation of motion is a generalized geodesic for non-rotating spherical objects.

Derivation is divergence-free and applicable in arbitrary backgrounds.

Results are consistent with prior studies.

Abstract

We give a straightforward and divergence free derivation of the equation of motion for a small but finite object in an arbitrary background using strong field point particle limit. The resulting equation becomes a generalized geodesic for a non-rotating spherical object which is consisitent with previous studies.