Electrodynamics in curved spacetime: Gravitationally-induced constitutive equations and the spacetime index of refraction

TL;DR

This paper extends the concept of spacetime index of refraction to full stationary spacetimes using three approaches, providing a comprehensive framework for understanding light propagation in curved spacetime.

Contribution

It introduces a novel formulation of the refractive index in stationary spacetimes through Fermat's principle, classical definitions, and constitutive equations, establishing their equivalence in different formalisms.

Findings

Refractive index defined for full stationary spacetimes.

Equivalence of threading and slicing formalism approaches.

Identification of gravitational analogs of toroidal moments and nonreciprocal refraction.

Abstract

Previous studies on spacetime index of refraction are mostly restricted to the static spacetimes. In this study we fill this gap by introducing the refractive index for full stationary spacetimes, employing three different approaches. These include applying Fermat's principle, employing the classical definition of refractive index, and using gravitationally-induced constitutive equations. These calculations are carried out in both threading and slicing spacetime decomposition formalisms, and their equivalence is stablished. We discuss possible applications of the spacetime index of refraction, specially in the study of light trajectories and their characteristics in stationary spacetimes. More specifically we show that there is a gravitational analog of a toroidal moment, and discuss possible gravitational analog of nonreciprocal refraction in materials with a toroidal domain wall.