The solutions of the Einstein equations for uniformly accelerated particles without nodal singularities. I. Freely falling particles in external fields

Abstract

Ernst’s procedure of removing the nodal singularity in the C-metric is applied to the solutions for uniformly accelerated particles of Bonnor & Swaminarayan ( Z . Phys . 177, 240 (1964)). A new solution representing two independent Curzon-Chazy particles falling freely in opposite directions in an external gravitational field is constructed. It is therefore not asymptotically flat. This solution is then shown to follow from the original solutions of Bonnor & Swaminarayan for two independent pairs of uniformly accelerated particles if a limiting procedure, namely removing one particle in each pair to infinity and increasing its mass simultaneously, is performed. In this manner, a clear physical interpretation is given both to generalized Bonnor & Swaminarayan solutions constructed here and to generalized C-metric solutions found by Ernst in 1978.