The gravitational field of a light wave

TL;DR

This paper explores the gravitational effects of light waves in Einstein-Maxwell theory, providing explicit metrics, analyzing test particle motion, and examining quantum particle behavior in these gravitational fields.

Contribution

It presents explicit solutions for the gravitational field of light waves and extends analysis to quantum particles, offering new insights into light-matter interactions in curved spacetime.

Findings

Explicit metric and curvature for polarized light waves

Test particles are scattered by light's gravitational field

Quantum energy spectrum in a circularly polarized 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.