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.

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