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We derive the gravitational waveform and gravitational-wave energy fluxgenerated by a binary star system of compact objects (neutron stars or blackholes), accurate through second post-Newtonian order ($O[(v/c)^4] \simO[(Gm/rc^2)^2]$) beyond the lowest-order quadrupole approximation. We cast theEinstein equations into the form of a flat-spacetime wave equation togetherwith a harmonic gauge condition, and solve it formally as a retarded integralover the past null cone of the chosen field point. The part of this integralthat involves the matter sources and the near-zone gravitational field isevaluated in terms of multipole moments using standard techniques; theremainder of the retarded integral, extending over the radiation zone, isevaluated in a novel way. The result is a manifestly convergent and finiteprocedure for calculating gravitational radiation to arbitrary orders in apost-Newtonian expansion. Through second post-Newtonian order, the radiation isalso shown to propagate toward the observer along true null rays of theasymptotically Schwarzschild spacetime, despite having been derived using flatspacetime wave equations. The method cures defects that plagued previous``brute- force'' slow-motion approaches to the generation of gravitationalradiation, and yields results that agree perfectly with those recently obtainedby a mixed post-Minkowskian post-Newtonian method. We display explicit formulaefor the gravitational waveform and the energy flux for two-body systems, bothin arbitrary orbits and in circular orbits. In an appendix, we extend theformalism to bodies with finite spatial extent, and derive the spin correctionsto the waveform and energy loss.Comment: 59 pages ReVTeX; Physical Review D, in press; figures available on  request to psp@howdy.wustl.ed

Gravitational radiation from compact binary systems: Gravitational waveforms and energy loss to second post-Newtonian order