Photon rockets and gravitational radiation

The absence of gravitational radiation in Kinnersley’s “photon rocket” solution of Einstein’s equations is clarified by studying the mathematically well-defined problem of point-like photon rockets in Minkowski space (i.e. massive particles emitting null fluid anisotropically and accelerating because of the recoil). We explicitly compute the (uniquely defined) linearized retarded gravitational waves emitted by such objects, which are the coherent superposition of the gravitational waves generated by the motion of the massive point-like rocket and of those generated by the energy-momentum distribution of the photon fluid. In the special case (corresponding to Kinnersley’s solution) where the anisotropy of the photon emission is purely dipolar we find that the gravitational wave amplitude generated by the energymomentum of the photons exactly cancels the usual 1/r gravitational