Einstein's Equations in Electromagnetic Media

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.

Figures (2)

• Figure 1: Visualisation of ADM foliation
• Figure 2: Visualisation of ADM constraint equations.