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

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

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

Numerical analysis of backreaction in acoustic black holes

Using methods of Quantum Field Theory in curved spacetime, the first order in hbar quantum corrections to the motion of a fluid in an acoustic black hole configuration are numerically computed. These corrections arise from the non linear backreaction of the emitted phonons. Time dependent (isolated system) and equilibrium configurations (hole in a sonic cavity) are both analyzed.Comment: 7 pages, 5 figure

Classical and Quantum Shell Dynamics, and Vacuum Decay

Following a minisuperspace approach to the dynamics of a spherically symmetric shell, a reduced Lagrangian for the radial degree of freedom is derived directly from the Einstein-Hilbert action. The key feature of this new Lagrangian is its invariance under time reparametrization. Indeed, all classical and quantum dynamics is encoded in the Hamiltonian constraint that follows from that invariance. Thus, at the classical level, we show that the Hamiltonian constraint reproduces, in a simple gauge, Israel's matching condition which governs the evolution of the shell. In the quantum case, the vanishing of the Hamiltonian (in a weak sense), is interpreted as the Wheeler-DeWitt equation for the physical states, in analogy to the corresponding case in quantum cosmology. Using this equation, quantum tunneling through the classical barrier is then investigated in the WKB approximation, and the connection to vacuum decay is elucidated.Comment: 36 pages, ReVTeX, 10 Figs. in postscript format, in print on Class.& Quant.Gra

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

Backreaction in Acoustic Black Holes

The backreaction equations for the linearized quantum fluctuations in an acoustic black hole are given. The solution near the horizon, obtained within a dimensional reduction, indicates that acoustic black holes, unlike Schwarzschild ones, get cooler as they radiate phonons. They show remarkable analogies with near-extremal Reissner-Nordstrom black holes.Comment: 4 pages, revtex, 1 figure. revised version, published in pr