A Note on the Coordinate Freedom in Describing the Motion of Particles   in General Relativity
  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. 
Samuel E. Gralla and Robert M. Wald
gr-qc