Covariant formulation of the post-1-Newtonian approximation to general relativity

@article{Tichy2011CovariantFO,
  title={Covariant formulation of the post-1-Newtonian approximation to general relativity},
  author={Wolfgang Tichy and Eanna E. Flanagan},
  journal={Physical Review D},
  year={2011},
  volume={84},
  pages={044038}
}
We derive a coordinate-independent formulation of the post-1-Newtonian approximation to general relativity. This formulation is a generalization of the Newton-Cartan geometric formulation of Newtonian gravity. It involves several fields and a connection, but no spacetime metric at the fundamental level. We show that the usual coordinate-dependent equations of post-Newtonian gravity are recovered when one specializes to asymptotically flat spacetimes and to appropriate classes of coordinates. 

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