A Note on the Coordinate Freedom in Describing the Motion of Particles in General Relativity
Samuel E. Gralla, Robert M. Wald
TL;DR
This paper analyzes the coordinate freedom in a framework for describing particle motion in general relativity, crucial for formulating equations of motion in various gauges.
Contribution
It provides an analysis of coordinate freedom within a previously developed framework for small body motion in general relativity.
Findings
Identifies the gauge freedoms in the framework.
Clarifies how equations of motion depend on coordinate choices.
Supports the formulation of gauge-invariant descriptions.
Abstract
Our previous work developed a framework for treating the motion of a small body in general relativity, based on a one-parameter-family of solutions to Einstein's equation. Here we give an analysis of the coordinate freedom allowed within this framework, as is needed to determine the form of the equations of motion when they are expressed in general gauges.
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