Einstein's Equations in Electromagnetic Media

TL;DR

This paper demonstrates how Einstein's equations can be encoded in electromagnetic media, enabling the simulation of gravitational phenomena through optical analogues.

Contribution

It extends Plebanski's mapping to represent Einstein equations in bianisotropic media and derives gravitational-wave analogues as medium perturbations.

Findings

Encoded Einstein equations in electromagnetic media using Plebanski's mapping.

Derived gravitational-wave analogues as perturbations in optical media.

Linearised equations in vacuum to simulate gravitational phenomena.

Abstract

In this paper, we extend Plebanski's mapping to encode the Einstein equations in ADM form within a bianisotropic electromagnetic medium. We realise this by translating the ADM constraints and evolution equations into dynamical conditions on the medium's constitutive parameters. These transformed equations are then linearised in vacuum to derive gravitational-wave analogues as perturbations of the optical medium.