Photon propagation in a material medium on a curved spacetime

TL;DR

This paper investigates how light propagates through a nonlinear dielectric medium around a charged, spherically symmetric mass in curved spacetime, revealing polarization-dependent effects on light trajectories and corrections to gravitational lensing.

Contribution

It introduces an effective geometry approach to describe light propagation in nonlinear media influenced by gravity, highlighting polarization effects and conformally flat metrics for negative polarization.

Findings

Different polarizations lead to distinct light trajectories.

Electromagnetic fields polarize the medium, affecting light's gravitational deflection.

Effective metric becomes conformally flat for negative polarization.

Abstract

We consider a nonlinear dielectric medium surrounding a static, charged and spherically symmetric compact body which gravitational field is driven by General Relativity (GR). Considering the propagating waves on the dielectric medium, we describe the trajectory of light as geodesics on an effective geometry given by Hadamard's discontinuities. We analyze some consequences of the effective geometry in the propagation of light, with relation to the predictions of the background gravitational field, that includes corrections on the geometrical redshift and on the gravitational deflection of light. We show that the background electromagnetic field polarize the material medium, such that different polarizations of light are distinguished by different corrections on these quantities. As a consequence, we have two possible paths for the trajectory of light in such configuration, that coincide if we turn off the electromagnetic field or if the permittivity is constant. We show that the effective metric associated to the negative polarization, for a given dependence of the dielectric permittivity, is conformally flat.