Light Rays at Optical Black Holes in Moving Media

Abstract

Light experiences a non-uniformly moving medium as an effective gravitational field, endowed with an effective metric tensor $\tilde{g}^{\mu \nu}=\eta^{\mu \nu}+(n^2-1)u^\mu u^\nu$, $n$ being the refractive index and $u^\mu$ the four-velocity of the medium. Leonhardt and Piwnicki [Phys. Rev. A {\bf 60}, 4301 (1999)] argued that a flowing dielectric fluid of this kind can be used to generate an 'optical black hole'. In the Leonhardt-Piwnicki model, only a vortex flow was considered. It was later pointed out by Visser [Phys. Rev. Lett. {\bf 85}, 5252 (2000)] that in order to form a proper optical black hole containing an event horizon, it becomes necessary to add an inward radial velocity component to the vortex flow. In the present paper we undertake this task: we consider a full spiral flow, consisting of a vortex component plus a radially infalling component. Light propagates in such a dielectric medium in a way similar to that occurring around a rotating black hole. We calculate, and show graphically, the effective potential versus the radial distance from the vortex singularity, and show that the spiral flow can always capture light in both a positive, and a negative, inverse impact parameter interval. The existence of a genuine event horizon is found to depend on the strength of the radial flow, relative to the strength of the azimuthal flow. A limitation of our fluid model is that it is nondispersive.