Covariant formulation of the post-1-Newtonian approximation to General Relativity

Abstract

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.

14 pages, no figures, minor corrections, to appear in Phys. Rev. D

References in corpus (2)

• Numerical relativity confronts compact neutron star binaries: a review and status report
• Post-Newtonian theory and the two-body problem

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