Geometric optics for a coupling model of the electromagnetic and gravitational fields

TL;DR

This paper introduces an effective spacetime framework that restores the validity of geometric optics laws in a coupled electromagnetic-gravitational model, resolving issues like superluminal photons and Lorentz invariance violations.

Contribution

It proposes an effective spacetime approach to recover standard geometric optics laws in a coupling model that otherwise violates them.

Findings

Wave vector becomes null and follows geodesics in the effective spacetime.

Polarization remains perpendicular to light rays.

Photon number conservation is maintained in the effective spacetime.

Abstract

The coupling between the electromagnetic and gravitational fields results in "faster than light" photons and invalids the Lorentz invariance and some laws of physics. A typical example is that the first and third laws of geometric optics are invalid in the usual spacetime. By introducing an effective spacetime, we find that the wave vector can be casted into null and then it obeys the geodesic equation, the polarization vector is perpendicular to the rays, and the number of photons is conserved. That is to say, the laws of geometric optics are still valid for the modified theory in the effective spacetime. We also show that the focusing theorem of light rays for the modified theory in the effective spacetime takes the same form as usual.