Dielectric analog space-times

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.

Figure 1

Electromagnetic fields $\widehat{\mathbf{F}}$ and $\widehat{\mathbf{G}}$ are pulled back from a patch of a curved, vacuum manifold to a material residing in Minkowski space-time by using the pullback ${\mathcal{T}}^{*}$.