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

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

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

Gray-body factor and infrared divergences in 1D BEC acoustic black holes

It is shown that the gray-body factor for a one-dimensional elongated Bose-Einstein condensate (BEC) acoustic black hole with one horizon does not vanish in the low-frequency ($\omega\to 0$) limit. This implies that the analog Hawking radiation is dominated by the emission of an infinite number ($\frac{1}{\omega}$) of soft phonons in contrast with the case of a Schwarzschild black hole where the gray-body factor vanishes as $\omega\to 0$ and the spectrum is not dominated by low-energy particles. The infrared behaviors of certain correlation functions are also discussed.Comment: 6 pages, 2 figures. Final version. A double misprint in Eq. (21) of the published version has been corrected her

Hawking radiation from extremal and non-extremal black holes

The relationship between Hawking radiation emitted by non extremal and extremal Reissner Nordstrom black holes is critically analyzed. A careful study of a series of regular collapsing geometries reveals that the stress energy tensor stays regular in the extremal limit and is smoothly connected to that of non extremal black holes. The unexpected feature is that the late time transients which played little role in the non extremal case are necessary to preserve the well defined character of the flux in the extremal case. The known singular behavior of the static energy density of extremal black holes is recovered from our series by neglecting these transients, when performing what turns out to be an illegitimate late time limit. Although our results are derived in two dimensional settings, we explain why they should also apply to higher dimensional black holes.Comment: 18 pages, late

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

Correlation patterns from massive phonons in 1+1 dimensional acoustic black holes: A toy model

Transverse excitations in analogue black holes induce a mass like term in the longitudinal mode equation. With a simple toy model we show that correlation functions display a rather rich structure characterized by groups of parallel peaks. For the most part the structure is completely different from that found in the massless case.Comment: 40 pages, 13 figures. Minor changes and corrections Phys. Rev. D versio

Quantum Effects in Black Hole Interiors

The Weyl curvature inside a black hole formed in a generic collapse grows, classically without bound, near to the inner horizon, due to partial absorption and blueshifting of the radiative tail of the collapse. Using a spherical model, we examine how this growth is modified by quantum effects of conformally coupled massless fields.Comment: 13 pages, 1 figure (not included), RevTe