  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.
