Uniformly Accelerating Charged Mass in General Relativity

Abstract

We discuss a type-{22} solution of the Einstein-Maxwell equations which represents the field of a uniformly accelerating charged point mass. It contains three arbitrary parameters $m$, $e$, and $A$, representing mass, charge, and acceleration, respectively. The solution is a direct generalization of the Reissner-Nordstrom solution of general relativity and the Born solution of classical electrodynamics. The external "mechanical" force necessary to produce the acceleration appears in the form of a timelike nodal two-surface extending from the particle's world line to infinity. This does not prevent us from regarding the solution as asymptotically flat and calculating the radiation pattern of its electromagnetic and gravitational waves. We find as well a maximal analytic extension of the solution and discuss its properties. Except for an extra "outer" Killing horizon due to the accelerated motion, the horizon structure closely resembles the Reissner-Nordstrom case.