Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order

Abstract

We derive the gravitational field and equations of motion of compact binary systems up to the 5/2 post-Newtonian approximation of general relativity (where radiation-reaction effects first appear). The approximate post-Newtonian gravitational field might be used in the problem of initial conditions for the numerical evolution of binary black-hole space-times. On the other hand we recover the Damour-Deruelle 2.5PN equations of motion of compact binary systems. Our method is based on an expression of the post-Newtonian metric valid for general (continuous) fluids. We substitute into the fluid metric the standard stress-energy tensor appropriate for a system of two point-like particles. We remove systematically the infinite self-field of each particle by means of the Hadamard partie finie regularization.

41 pages to appear in Physical Review D

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• 3rd post-Newtonian higher order Hamilton dynamics for two-body point-mass systems
• Computing the merger of black-hole binaries: the IBBH problem

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