4D quantum black hole physics from 2D models?

Minimally coupled 4D scalar fields in Schwarzschild space-time are considered. Dimensional reduction to 2D leads to a well known anomaly induced effective action, which we consider here in a local form with the introduction of auxiliary fields. Boundary conditions are imposed on them in order to select the appropriate quantum states (Boulware, Unruh annd Israel-Hartle-Hawking). The stress tensor is then calculated and its comparison with the expected 4D form turns out to be unsuccessful. We also critically discuss in some detail a recent controversial result appeared in the literature on the same topic.Comment: latex, 13 pages; misprints corrected, references adde

The depletion in Bose Einstein condensates using Quantum Field Theory in curved space

Using methods developed in Quantum Field Theory in curved space we can estimate the effects of the inhomogeneities and of a non vanishing velocity on the depletion of a Bose Einstein condensate within the hydrodynamical approximation.Comment: 4 pages, no figure. Discussion extended and references adde

Amplifying the Hawking signal in BECs

We consider simple models of Bose-Einstein condensates to study analog pair-creation effects, namely the Hawking effect from acoustic black holes and the dynamical Casimir effect in rapidly time-dependent backgrounds. We also focus on a proposal by Cornell to amplify the Hawking signal in density-density correlators by reducing the atoms' interactions shortly before measurements are made.Comment: 10 pages, 3 figures; to appear in Advances in High Energy Physics, special Issue 'Experimental Tests of Quantum Gravity and Exotic Quantum Field Theory Effects

On the Dimensional Reduction Procedure

The issue related to the so-called dimensional reduction procedure is revisited within the Euclidean formalism. First, it is shown that for symmetric spaces, the local exact heat-kernel density is equal to the reduced one, once the harmonic sum has been succesfully performed. In the general case, due to the impossibility to deal with exact results, the short time heat-kernel asymptotics is considered. It is found that the exact heat-kernel and the dimensionally reduced one coincide up to two non trivial leading contributions in the short time expansion. Implications of these results with regard to dimensional-reduction anomaly are discussed.Comment: 15 pages, Latex, enlarged discussion added in Sec 3 and typos corrected. Version to appear in Nucl. Phys.

Particle production and transplanckian problem on the non-commutative plane

We consider the coherent state approach to non-commutativity, and we derive from it an effective quantum scalar field theory. We show how the non-commutativity can be taken in account by a suitable modification of the Klein-Gordon product, and of the equal-time commutation relations. We prove that, in curved space, the Bogolubov coefficients are unchanged, hence the number density of the produced particle is the same as for the commutative case. What changes though is the associated energy density, and this offers a simple solution to the transplanckian problem.Comment: Minor typos corrected, references added. Accepted for publication by Modern Physics Letter

Hawking effect in BECs acoustic white holes

Bogoliubov pseudoparticle creation in a BEC undergoing a WH like flow is investigated analytically in the case of a one dimensional geometry with stepwise homogeneous regions. Comparison of the results with those corresponding to a BH flow is performed. The implications for the analogous gravitational problem is discussed.Comment: 29 pages, 32 figure

Generalized Virasoro anomaly and stress tensor for dilaton coupled theories

We derive the anomalous transformation law of the quantum stress tensor for a 2D massless scalar field coupled to an external dilaton. This provides a generalization of the Virasoro anomaly which turns out to be consistent with the trace anomaly. We apply it together with the equivalence principle to compute the expectation values of the covariant quantum stress tensor on a curved background. Finally we briefly illustrate how to evaluate vacuum polarization and Hawking radiation effects from these results.Comment: enlarged version of hep-th/0307096 containing the quantum stress tensor for arbitrary geometries and discussion of the Hawking effect. To appear in Phys. Lett.

Low frequency gray-body factors and infrared divergences: rigorous results

Formal solutions to the mode equations for both spherically symmetric black holes and Bose-Einstein condensate acoustic black holes are obtained by writing the spatial part of the mode equation as a linear Volterra integral equation of the second kind. The solutions work for a massless minimally coupled scalar field in the s-wave or zero angular momentum sector for a spherically symmetric black hole and in the longitudinal sector of a 1D Bose-Einstein condensate acoustic black hole. These solutions are used to obtain in a rigorous way analytic expressions for the scattering coefficients and gray-body factors in the zero frequency limit. They are also used to study the infrared behaviors of the symmetric two-point function and two functions derived from it: the point-split stress-energy tensor for the massless minimally coupled scalar field in Schwarzschild-de Sitter spacetime and the density-density correlation function for a Bose-Einstein condensate acoustic black hole.Comment: 41 pages, 5 figure

Scattering coefficients and gray-body factor for 1D BEC acoustic black holes: exact results

A complete set of exact analytic solutions to the mode equation is found in the region exterior to the acoustic horizon for a class of 1D Bose-Einstein condensate (BEC) acoustic black holes. From these, analytic expressions for the scattering coefficients and gray-body factor are obtained. The results are used to verify previous predictions regarding the behaviors of the scattering coefficients and gray-body factor in the low frequency limit.Comment: 13 pages, 1 figure, Final version, to appear in Phys. Rev.