Anisotropic metamaterial as an analogue of a black hole

Propagation of light in a metamaterial medium which mimics curved spacetime and acts like a black hole is studied. We show that for a particular type of spacetimes and wave polarization, the time dilation appears as dielectric permittivity, while the spatial curvature manifests as magnetic permeability. The optical analogue to the relativistic Hamiltonian which determines the ray paths (null geodesics) in the anisotropic metamaterial is obtained. By applying the formalism to the Schwarzschild metric, we compare the ray paths with full-wave simulations in the equivalent optical medium.