  It is has been long known that the curved space in the presence of
gravitation can be described as a non-homogeneous anisotropic medium in flat
geometry with different constitutive equations. In this article, we show that
the eigenpolarizations of such medium can be exactly solved, leading to a
pseudo-isotropic description of curved vacuum with two refractive index
eigenvalues having opposite signs, which correspond to forward and backward
travel in time. We conclude that for a rotating universe, time-reversal
symmetry is broken. We also demonstrate the applicability of this method to
Schwarzschild metric and derive exact forms of refractive index. We derive the
subtle optical anisotropy of space around a spherically symmetric, non-rotating
and uncharged blackhole in the form of an elegant closed form expression, and
show that the refractive index in such a pseudo-isotropic system would be a
function of coordinates as well as the direction of propagation. Corrections
arising from such anisotropy in the bending of light are shown and a simplified
system of equations for ray-tracing in the equivalent medium of Schwarzschild
metric is found.
