Einstein's Equations in Electromagnetic Media
arXiv:2508.11300 · doi:10.1209/0295-5075/ae58cf
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.