Formation of a sonic horizon in isotropically expanding Bose-Einstein condensates

We propose a simple experiment to create a sonic horizon in isotropically trapped cold atoms within currently available experimental techniques. Numerical simulation of the Gross-Pitaevskii equation shows that the sonic horizon should appear by making the condensate expand. The expansion is triggered by changing the interaction which can be controlled by the Feshbach resonance in real experiments. The sonic horizon is shown to be quasi-static for sufficiently strong interaction or large number of atoms. The characteristic temperature that is associated with particle emission from the horizon, which corresponds to the Hawking temperature in an ideal situation, is estimated to be a few nK.Comment: 7 pages, 8 figures; Final version, accepted to Phys.Rev.

From vacuum fluctuations across an event horizon to long distance correlations

We study the stress energy two-point function to show how short distance correlations across the horizon transform into correlations among asymptotic states, for the Unruh effect, and for black hole radiation. In the first case the transition is caused by the coupling to accelerated systems. In the second, the transition is more elusive and due to the change of the geometry from the near horizon region to the asymptotic one. The gradual transition is appropriately described by using affine coordinates. We relate this to the covariant regularization used to evaluate the mean value of the stress energy. We apply these considerations to analogue black holes, i.e. dispersive theories. On one hand, the preferred rest frame gives further insight about the transition, and on the other hand, the dispersion tames the singular behavior found on the horizon in relativistic theories.Comment: 21 pages, 4 figures, new section on growth of correlation

Quasi-normal mode analysis in BEC acoustic black holes

We perform a quasi-normal mode analysis of black hole configurations in Bose-Einstein condensates (BEC). In this analysis we use the full Bogoliubov dispersion relation, not just the hydrodynamic or geometric approximation. We restrict our attention to one-dimensional flows in BEC with step-like discontinuities. For this case we show that in the hydrodynamic approximation quasi-normal modes do not exist. The full dispersion relation, however, allows the existence of quasi-normal modes. Remarkably, the spectrum of these modes is not discrete but continuous.Comment: 7 pages, 3 figure

Quantum Non-Gravity and Stellar Collapse

Observational indications combined with analyses of analogue and emergent gravity in condensed matter systems support the possibility that there might be two distinct energy scales related to quantum gravity: the scale that sets the onset of quantum gravitational effects $E_B$ (related to the Planck scale) and the much higher scale $E_L$ signalling the breaking of Lorentz symmetry. We suggest a natural interpretation for these two scales: $E_L$ is the energy scale below which a special relativistic spacetime emerges, $E_B$ is the scale below which this spacetime geometry becomes curved. This implies that the first `quantum' gravitational effect around $E_B$ could simply be that gravity is progressively switched off, leaving an effective Minkowski quantum field theory up to much higher energies of the order of $E_L$. This scenario may have important consequences for gravitational collapse, inasmuch as it opens up new possibilities for the final state of stellar collapse other than an evaporating black hole.Comment: 6 pages, 2 figures. v2: Partially restructured; potentially observable consequence added. Several clarifications + 3 new references. To appear in Found. of Phy

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

Wormhole effective interactions in anti-de Sitter spacetime

The effects of asymptotically anti-de Sitter wormholes in low-energy field theory are calculated in full detail for three different matter contents: a conformal scalar field, an electromagnetic field and gravitons. There exists a close relation between the choice of vacuum for the matter fields and the selection of a basis of the Hilbert space of anti-de Sitter wormholes. In the presence of conformal matter (i.e., conformal scalar or electromagnetic fields), this relation allows us to interpret the elements of these bases as wormhole states containing a given number of particles. This interpretation is subject to the same kind of ambiguity in the definition of particle as that arising from quantum field theory in curved spacetime. In the case of gravitons, owing to the non-conformal coupling, it is not possible to describe wormhole states in terms of their particle content

Analog model for an expanding universe

Over the last few years numerous papers concerning analog models for gravity have been published. It was shown that the dynamical equation of several systems (e.g. Bose-Einstein condensates with a sink or a vortex) have the same wave equation as light in a curved-space (e.g. black holes). In the last few months several papers were released which deal with simulations of the universe. In this article the de-Sitter universe will be compared with a freely expanding three-dimensional spherical Bose-Einstein condensate. Initially the condensate is in a harmonic trap, which suddenly will be switched off. At the same time a small perturbation will be injected in the center of the condensate cloud. The motion of the perturbation in the expanding condensate will be discussed, and after some transformations the similarity to an expanding universe will be shown.Comment: Presented at the 4th Australasian conference on General Relativity and Cosmology, Monash U, Melbourne, 7-9 January 200

On the robustness of acoustic black hole spectra

We study the robustness of the spectrum emitted by an acoustic black hole by considering series of stationary flows that become either subsonic or supersonic, i.e. when the horizon disappears. We work with the superluminal Bogoliubov dispersion of Bose--Einstein condensates. We find that the spectrum remains remarkably Planckian until the horizon disappears. When the flow is everywhere supersonic, new pair creation channels open. This will be the subject of a forthcoming work.Comment: 4 pages, 2 figure, jpconf.cls; to appear in the proceedings of the Spanish Relativity Meeting ERE201