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.

30 pages, LaTeX, 4 ps figures. Expanded discussion especially in section 6; 5 new references. Version to appear in Phys. Rev. D

References in corpus (1)

• Analog gravity from field theory normal modes?

Cited by in corpus (21)

• Analogue Gravity
• Hawking radiation in an electro-magnetic wave-guide?
• Quantum Physics of Simple Optical Instruments
• On Slow Light as a Black Hole Analogue
• Acoustic black holes in a two-dimensional "photon-fluid"
• Dielectric black holes induced by a refractive index perturbation and the Hawking effect
• Analog gravity from electrodynamics in non-linear media
• Dirac Equation in (1+1)-Dimensional Curved Spacetime and the Multiphoton Quantum Rabi Model
• Analogue gravity and the Hawking effect: historical perspective and literature review
• Spacetime geometries and light trapping in travelling refractive index perturbations
• On optical black holes in moving dielectrics
• Birefringence in nonlinear anisotropic dielectric media
• Geometric Phase for Fermionic Quasiparticles Scattering by Disgyration in Superfluids
• Metric Relativity and the Dynamical Bridge: highlights of Riemannian geometry in physics
• Dynamics of an Acoustic Black Hole as an Open Quantum System
• Decoherence and Loss of Entanglement in Acoustic Black Holes
• A possible approach on optical analogues of gravitational attractors
• Scaterring of Massless Quasiparticles in the 3He-A Superfluid
• Criterion for testing the covariance of physical laws and Gordon optical metric
• On a pragmatic approach optical analogues of gravitational attractors
• The spin-orbit interaction and the spin-spin interaction of photons in an inhomogeneous medium