Dielectric Analog Space-Times

TL;DR

This paper develops a generalized framework for creating dielectric analog models of arbitrary space-times, including rotating black holes, using metamaterials to simulate complex gravitational geometries in laboratory settings.

Contribution

It extends previous models to non-static space-times and establishes a flexible correspondence between electrodynamics in curved space-times and in dielectric media.

Findings

Dielectric analogs of Kerr geometry are reproducible with regular dielectrics.

The mapping between curved space-time electrodynamics and dielectric media is non-unique.

The approach enables simulation of complex gravitational fields using metamaterials.

Abstract

We generalize the notion of a dielectric analog Schwarzschild black hole model to analog models of arbitrary space-times; in particular, the approach is not restricted to static space-times. This is done by establishing a correspondence between electrodynamics on a curved, vacuum manifold, with electrodynamics in a general linear dielectric residing in Minkowski space-time. The mapping is not unique, allowing for some freedom in the specification of equivalent materials, which could be useful for exploiting recent developments in the production of metamaterials. Some examples are considered, with special attention paid to the dielectric analog of the exterior Kerr geometry, which is found to be reproducible with regular, linear, dielectrics.