Gravitational radiation from an accelerating massive particle in general relativity

A comprehensive description is given of a spacetime model of an accelerating massive particle. The particle radiates gravitational waves with optical shear. The wave fronts are smoothly deformed spheres and the particle experiences radiation reaction, similar to an accelerating charged particle, and a loss of mass described by a Bondi mass-loss formula. The spacetime is one of the Bondi–Sachs forms but presented in a form here which is particularly suited to the construction of the model particle. All details of the calculations are given. A detailed examination of the gravitational field of the particle is provided which illustrates the presence of gravitational radiation and also exhibits, in the form of a type of singularity found in some Robinson–Trautman spacetimes, the absence of an external field to supply energy to the particle.