Graviton mediated photon-photon scattering in general relativity

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 discrepancies are explained.

Figure 1

Polarization directions and the definition of the scattering angle $\theta$.

Figure 2

The classical (solid line) and quantum field theoretical (dashed line) cross-sections in arbitrary units as a function of scattering angle.

Figure 3

The ratio of the classical and quantum field theoretical cross-sections ${\sigma }_1$ and ${\sigma }_2$, respectively, as a function of scattering angle.