The gravitational interaction of light: from weak to strong fields

TL;DR

This paper explores the nonlinear gravitational interactions of light and gravitational waves, revealing conditions for linear superposition and quantifying photon-photon attraction in general relativity.

Contribution

It provides a new explanation for the linear superposition of parallel pp-waves and quantifies light-to-light attraction, including a proven conjecture relating different interaction strengths.

Findings

Parallel pp-waves do not interact due to force cancellation.

Photon-to-photon attraction is twice matter-to-light attraction.

Light-to-light attraction is four times matter-to-matter attraction.

Abstract

An explanation is proposed for the fact that pp-waves superpose linearly when they propagate parallely, while they interact nonlinearly, scatter and form singularities or Cauchy horizons if they are antiparallel. Parallel pp-waves do interact, but a generalized gravitoelectric force is exactly cancelled by a gravitomagnetic force. In an analogy, the interaction of light beams in linearized general relativity is also revisited and clarified, a new result is obtained for photon to photon attraction, and a conjecture is proved. Given equal energy density in the beams, the light-to-light attraction is twice the matter-to-light attraction and four times the matter-to-matter attraction.