Graviton mediated photon-photon scattering in general relativity

TL;DR

This paper investigates photon-photon scattering mediated by gravitons within general relativity, analyzing four-wave interactions of electromagnetic waves influenced by gravitational perturbations, and compares classical and quantum approaches.

Contribution

It provides a perturbative solution to the Einstein-Maxwell system for photon interactions mediated by gravity, including arbitrary polarizations and a comparison with quantum field theory results.

Findings

Derived coupling coefficients for arbitrary polarizations.

Identified small discrepancies with quantum calculations and explained them.

Extended understanding of photon-photon interactions in gravitational contexts.

Abstract

In this paper we consider photon-photon scattering due to self-induced gravitational perturbations on a Minkowski background. We focus on four-wave interaction between plane waves with weakly space and time dependent amplitudes, since interaction involving a fewer number of waves is excluded by energy-momentum conservation. The Einstein-Maxwell system is solved perturbatively to third order in the field amplitudes and the coupling coefficients are found for arbitrary polarizations in the center of mass system. Comparisons with calculations based on quantum field theoretical methods are made, and the small discrepances are explained.