PHOTON ROCKETS MOVING ARBITRARILY IN ANY DIMENSION

Abstract

A family of explicit exact solutions of Einstein's equations in four and higher dimensions is studied which describes the gravitational field of an object accelerating due to an anisotropic emission of photons. It is possible to prescribe an arbitrary motion, so that the acceleration of such photon rocket need not be uniform — both its magnitude and direction may vary with time. Except at the location of the rocket the space–times have no curvature singularities, and topological defects like cosmic strings are also absent. Any value of a cosmological constant is allowed. We investigate some particular examples of motion, namely a straight flight and a circular trajectory, and we derive the corresponding radiation patterns and the mass loss of the rockets. We also demonstrate the absence of "gravitational aberration" in such space–times. This interesting member of the higher-dimensional Robinson–Trautman class of pure radiation space–times of algebraic Type D generalizes the class of Kinnersley's solutions that has long been known in four-dimensional general relativity.