Comment on "Relativistic Effects of Light in Moving Media with Extremely Low Group Velocity"

In [cond-mat/9906332; Phys. Rev. Lett. 84, 822 (2000)] and [physics/9906038; Phys. Rev. A 60, 4301 (1999)] Leonhardt and Piwnicki have presented an interesting analysis of how to use a flowing dielectric fluid to generate a so-called "optical black hole". Qualitatively similar phenomena using acoustical processes have also been much investigated. Unfortunately there is a subtle misinterpretation in the Leonhardt-Piwnicki analysis regarding these "optical black holes": While it is clear that "optical black holes" can certainly exist as theoretical constructs, and while the experimental prospects for actually building them in the laboratory are excellent, the particular model geometries that Leonhardt and Piwnicki write down as alleged examples of "optical black holes" are in fact not black holes at all.Comment: one page comment, uses ReV_TeX 3; discussion clarified; basic physical results unaltere

Warped space-time for phonons moving in a perfect nonrelativistic fluid

We construct a kinematical analogue of superluminal travel in the ``warped'' space-times curved by gravitation, in the form of ``super-phononic'' travel in the effective space-times of perfect nonrelativistic fluids. These warp-field space-times are most easily generated by considering a solid object that is placed as an obstruction in an otherwise uniform flow. No violation of any condition on the positivity of energy is necessary, because the effective curved space-times for the phonons are ruled by the Euler and continuity equations, and not by the Einstein field equations.Comment: 7 pages, 1 figure. Version as published; references update

Gravitational vacuum polarization III: Energy conditions in the (1+1) Schwarzschild spacetime

Building on a pair of earlier papers, I investigate the various point-wise and averaged energy conditions for the quantum stress-energy tensor corresponding to a conformally-coupled massless scalar field in the in the (1+1)-dimensional Schwarzschild spacetime. Because the stress-energy tensors are analytically known, I can get exact results for the Hartle--Hawking, Boulware, and Unruh vacua. This exactly solvable model serves as a useful sanity check on my (3+1)-dimensional investigations wherein I had to resort to a mixture of analytic approximations and numerical techniques. Key results in (1+1) dimensions are: (1) NEC is satisfied outside the event horizon for the Hartle--Hawking vacuum, and violated for the Boulware and Unruh vacua. (2) DEC is violated everywhere in the spacetime (for any quantum state, not just the standard vacuum states).Comment: 7 pages, ReV_Te

The sonic analogue of black hole radiation

A microscopic description of Hawking radiation in sonic black holes has been recently presented (Giovanazzi S 2005 Phys. Rev. Lett. 94 061302). This exactly solvable model is formulated in terms of one-dimensional scattering of a Fermi gas. In this paper, the model is extended to account possible finite size effects of a realistic geometry. The flow of particles is maintained by a piston (i.e. an impenetrable barrier) moving slowly towards the sonic horizon. Using existing technologies the Hawking temperature can be of order of a few microkelvin in a realistic experiment.Comment: 14 pages, 7 figures, submitted to Journal of Physics B: Atomic, Molecular & Optical Physic

From wormhole to time machine: Comments on Hawking's Chronology Protection Conjecture

The recent interest in ``time machines'' has been largely fueled by the apparent ease with which such systems may be formed in general relativity, given relatively benign initial conditions such as the existence of traversable wormholes or of infinite cosmic strings. This rather disturbing state of affairs has led Hawking to formulate his Chronology Protection Conjecture, whereby the formation of ``time machines'' is forbidden. This paper will use several simple examples to argue that the universe appears to exhibit a ``defense in depth'' strategy in this regard. For appropriate parameter regimes Casimir effects, wormhole disruption effects, and gravitational back reaction effects all contribute to the fight against time travel. Particular attention is paid to the role of the quantum gravity cutoff. For the class of model problems considered it is shown that the gravitational back reaction becomes large before the Planck scale quantum gravity cutoff is reached, thus supporting Hawking's conjecture.Comment: 43 pages,ReV_TeX,major revision

Analog black holes in flowing dielectrics

We show that a flowing dielectric medium with a linear response to an external electric field can be used to generate an analog geometry that has many of the formal properties of a Schwarzschild black hole for light rays, in spite of birefringence. We also discuss the possibility of generating these analog black holes in the laboratory.Comment: Revtex4 file, 7 pages, 4 eps figures, a few changes in presentation, some references added, conclusions unchange

On optical black holes in moving dielectrics

We study the optical paths of the light rays propagating inside a nonlinear moving dielectric media. For the rapidly moving dielectrics we show the existence of a distinguished surface which resembles, as far as the light propagation is concerned, the event horizon of a black hole. Our analysis clarifies the physical conditions under which electromagnetic analogues of the gravitational black holes can eventually be obtained in laboratory.Comment: 5 pages, 2 figures, revtex

Bounding the Hubble flow in terms of the w parameter

The last decade has seen increasing efforts to circumscribe and bound the cosmological Hubble flow in terms of model-independent constraints on the cosmological fluid - such as, for instance, the classical energy conditions of general relativity. Quite a bit can certainly be said in this regard, but much more refined bounds can be obtained by placing more precise constraints (either theoretical or observational) on the cosmological fluid. In particular, the use of the w-parameter (w=p/rho) has become increasingly common as a surrogate for trying to say something about the cosmological equation of state. Herein we explore the extent to which a constraint on the w-parameter leads to useful and nontrivial constraints on the Hubble flow, in terms of constraints on density rho(z), Hubble parameter H(z), density parameter Omega(z), cosmological distances d(z), and lookback time T(z). In contrast to other partial results in the literature, we carry out the computations for arbitrary values of the space curvature k in [-1,0,+1], equivalently for arbitrary Omega_0 <= 1.Comment: 15 page

Light Rays at Optical Black Holes in Moving Media

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

Quantum Field Theory Constrains Traversable Wormhole Geometries

Recently a bound on negative energy densities in four-dimensional Minkowski spacetime was derived for a minimally coupled, quantized, massless, scalar field in an arbitrary quantum state. The bound has the form of an uncertainty principle-type constraint on the magnitude and duration of the negative energy density seen by a timelike geodesic observer. When spacetime is curved and/or has boundaries, we argue that the bound should hold in regions small compared to the minimum local characteristic radius of curvature or the distance to any boundaries, since spacetime can be considered approximately Minkowski on these scales. We apply the bound to the stress-energy of static traversable wormhole spacetimes. Our analysis implies that either the wormhole must be only a little larger than Planck size or that there is a large discrepancy in the length scales which characterize the wormhole. In the latter case, the negative energy must typically be concentrated in a thin band many orders of magnitude smaller than the throat size. These results would seem to make the existence of macroscopic traversable wormholes very improbable.Comment: 26 pages, plain LaTe