The solutions of the Einstein equations for uniformly accelerated particles without nodal singularities. II. Self-accelerating particles

Abstract

Solutions are given representing two independent particles uniformly accelerated in opposite directions; the accelerations are not produced by nodal singularities, which are absent. One solution is constructed from the solution of Bonnor & Swaminarayan ( Z . Phys . 177, 240 (1964)) for two pairs of uniformly accelerated particles by a limiting procedure. Other solutions are obtained by solving the Einstein equations directly. A general solution representing two accelerating particles with arbitrary multipole structure attached to nodal singularities is first given. Then a condition restricting multipole moments is found, and this causes the nodal singularities to disappear. Although solutions of this type do not involve very physical sources, they belong to the best model space-times available today for examining the general theory of the asymptotic structure and the theory of gravitational radiation. Owing to the boost-rotation symmetry, the ADM 4-momentum at spatial infinity vanishes.