Three classes of space-time with a uniformly accelerating and nonrotating gravitational source

Abstract

Three classes of Petrov type-D nonrotating empty spaces, which we denote asA+*,A−*, anda0*, can be seen to represent, respectively, a gravitational field of a uniformly accelerating source which moves with velocity slower, faster than, or equal to that of light. The first two classes of space-time,A+* andA−*, approach to the last one,a0*, as the acceleration becomes greater and greater. The inertial frame in a flat space-time, relative to which a faster-thanlight particle moving along a spacelike geodesic behaves as an ordinary particle, is given and discussed. The behaviors of Killing horizons in the classes,A+* andA−* are investigated. Comparisons are made between the analysis by Farhoosh and Zimmerman and ours. Our identification of the acceleration parameter seems to be more appropriate than that by the above authors.