Optical Anisotropy of Schwarzschild Metric within Equivalent Medium Framework

TL;DR

This paper models the curved spacetime around blackholes as an anisotropic optical medium, deriving exact refractive indices and analyzing light bending, revealing subtle anisotropies and breaking of time-reversal symmetry in rotating universes.

Contribution

It provides an exact solution for the eigenpolarizations and refractive indices of Schwarzschild spacetime within an equivalent medium framework, including effects of anisotropy and rotation.

Findings

Exact refractive index expressions for Schwarzschild metric

Demonstration of optical anisotropy around blackholes

Corrections to light bending due to anisotropy

Abstract

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.