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We derive the gravitational field and equations of motion of compact binarysystems up to the 5/2 post-Newtonian approximation of general relativity (whereradiation-reaction effects first appear). The approximate post-Newtoniangravitational field might be used in the problem of initial conditions for thenumerical evolution of binary black-hole space-times. On the other hand werecover the Damour-Deruelle 2.5PN equations of motion of compact binarysystems. Our method is based on an expression of the post-Newtonian metricvalid for general (continuous) fluids. We substitute into the fluid metric thestandard stress-energy tensor appropriate for a system of two point-likeparticles. We remove systematically the infinite self-field of each particle bymeans of the Hadamard partie finie regularization.Comment: 41 pages to appear in Physical Review

physical review. d. particles, fields, gravitation, and cosmology/physical review. d. particles and fields

Gravitational field and equations of motion of compact binaries to<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mn>5</mml:mn><mml:mo>/</mml:mo><mml:mn>2</mml:mn></mml:math>post-Newtonian order

Gravitational field and equations of motion of compact binaries to5/2post-Newtonian order