The gravitational field of a light wave

Abstract

According to the classical Einstein-Maxwell theory of gravity and electromagnetism, a light-wave traveling in empty space-time is accompanied by a gravitational field of the pp-type. Therefore point masses are scattered by a light wave, even if they carry no electric or magnetic charge, or dipole moment. In this paper I present the explicit form of the metric and curvature for both circularly and linearly polarized light, and discuss the geodesic motion of test masses. This is followed by a discussion of classical scattering of point particles by the gravitational field associated with a circularly polarized electromagnetic block wave. A generalization to a quantum theory of particles in the background of these classical wave fields is presented in terms of the covariant Klein-Gordon equation. I derive the energy spectrum of quantum particles in the specific case of the circularly polarized block wave. Finally, a few general remarks on the extension to a quantum light wave are presented.