Analytical Theory of Optical Black Hole Analogues

Abstract

We develop an analytical formalism for studying optical analogues of spherically symmetric black-hole spacetimes. We demonstrate the exact similarity between the electromagnetic wave equations in an inhomogeneous medium in flat spacetime and those in a general-relativistic curved spacetime respectively. The permittivity and the permeability of an inhomogeneous optical medium act as metric components of the analogue spacetime. Manifest properties of black holes like curved light trajectories follow directly from our formalism. Other black-hole phenomena like quasinormal modes can also be studied within this framework. We extend the above formalism and obtain an approximate analogue for the case of purely dielectric media. These optical black holes can be employed to investigate black-hole phenomena with table-top experiments.