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Gravitational radiation reaction forces and balance equations for energy andmomenta are investigated to 3/2 post-Newtonian (1.5PN) order beyond thequadrupole approximation, corresponding to the 4PN order in the equations ofmotion of an isolated system. By matching a post-Newtonian solution for thegravitational field inside the system to a post-Minkowskian solution (obtainedin a previous work) for the gravitational field exterior to the system, wedetermine the 1PN relativistic corrections to the ``Newtonian" radiationreaction potential of Burke and Thorne. The 1PN reaction potential involvesboth scalar and vectorial components, with the scalar component depending onthe mass-type quadrupole and octupole moments of the system, and the vectorialcomponent depending in particular on the current-type quadrupole moment. In thecase of binary systems, the 1PN radiation reaction potential has been shown toyield consistent results for the 3.5PN approximation in the binary's equationsof motion. Adding up the effects of tails, the radiation reaction is thenwritten to 1.5PN order. In this paper, we establish the validity to 1.5PNorder, for general systems, of the balance equations relating the losses ofenergy, linear momentum, and angular momentum in the system to thecorresponding fluxes in the radiation field far from the system.Comment: To appear in Phys. Rev.

Gravitational radiation reaction and balance equations to post-Newtonian order