Gravitational field and equations of motion of compact binaries to 5/2 post-Newtonian order - art. no. 124002

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-Newton ian 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 b inary systems. Our method is based on an expression of the post-Newtonian m etric valid for general (continuous) fluids. We substitute into the fluid m etric the standard stress-energy tensor appropriate for a system of two poi ntlike particles. We remove systematically the infinite self-field of each particle by means of the Hadamard finite part regularization. [S0556-2821(9 8)08820-1].