Comparison of area spectra in loop quantum gravity

We compare two area spectra proposed in loop quantum gravity in different approaches to compute the entropy of the Schwarzschild black hole. We describe the black hole in general microcanonical and canonical area ensembles for these spectra. We show that in the canonical ensemble, the results for all statistical quantities for any spectrum can be reproduced by a heuristic picture of Bekenstein up to second order. For one of these spectra - the equally-spaced spectrum - in light of a proposed connection of the black hole area spectrum to the quasinormal mode spectrum and following hep-th/0304135, we present explicit calculations to argue that this spectrum is completely consistent with this connection. This follows without requiring a change in the gauge group of the spin degrees of freedom in this formalism from SU(2) to SO(3). We also show that independent of the area spectrum, the degeneracy of the area observable is bounded by $C A\exp(A/4)$, where $A$ is measured in Planck units and $C$ is a constant of order unity.Comment: 8 pages, Revtex 4, version to appear in Classical and Quantum Gravit

Black hole spectroscopy from Loop Quantum Gravity models

Using Monte Carlo simulations, we compute the integrated emission spectra of black holes in the framework of Loop Quantum Gravity (LQG). The black hole emission rates are governed by the entropy whose value, in recent holographic loop quantum gravity models, was shown to agree at leading order with the Bekenstein-Hawking entropy. Quantum corrections depend on the Barbero-Immirzi parameter $\gamma$. Starting with black holes of initial horizon area $A \sim 10^2$ in Planck units, we present the spectra for different values of $\gamma$. Each spectrum clearly decomposes in two distinct parts: a continuous background which corresponds to the semi-classical stages of the evaporation and a series of discrete peaks which constitutes a signature of the deep quantum structure of the black hole. We show that $\gamma$ has an effect on both parts that we analyze in details. Finally, we estimate the number of black holes and the instrumental resolution required to experimentally distinguish between the considered models.Comment: 11 pages, 9 figure

On the Nature of Black Holes in Loop Quantum Gravity

A genuine notion of black holes can only be obtained in the fundamental framework of quantum gravity resolving the curvature singularities and giving an account of the statistical mechanical, microscopic degrees of freedom able to explain the black hole thermodynamical properties. As for all quantum systems, a quantum realization of black holes requires an operator algebra of the fundamental observables of the theory which is introduced in this study based on aspects of loop quantum gravity. From the eigenvalue spectra of the quantum operators for the black hole area, charge and angular momentum, it is demonstrated that a strict bound on the extensive parameters, different from the relation arising in classical general relativity, holds, implying that the extremal black hole state can neither be measured nor can its existence be proven. This is, as turns out, a result of the specific form of the chosen angular momentum operator and the corresponding eigenvalue spectrum, or rather the quantum measurement process of angular momentum. Quantum mechanical considerations and the lowest, non-zero eigenvalue of the loop quantum gravity black hole mass spectrum indicate, on the one hand, a physical Planck scale cutoff of the Hawking temperature law and, on the other hand, give upper and lower bounds on the numerical value of the Immirzi parameter. This analysis provides an approximative description of the behavior and the nature of quantum black holes

Coherent states, constraint classes, and area operators in the new spin-foam models

Recently, two new spin-foam models have appeared in the literature, both motivated by a desire to modify the Barrett-Crane model in such a way that the imposition of certain second class constraints, called cross-simplicity constraints, are weakened. We refer to these two models as the FKLS model, and the flipped model. Both of these models are based on a reformulation of the cross-simplicity constraints. This paper has two main parts. First, we clarify the structure of the reformulated cross-simplicity constraints and the nature of their quantum imposition in the new models. In particular we show that in the FKLS model, quantum cross-simplicity implies no restriction on states. The deeper reason for this is that, with the symplectic structure relevant for FKLS, the reformulated cross-simplicity constraints, in a certain relevant sense, are now \emph{first class}, and this causes the coherent state method of imposing the constraints, key in the FKLS model, to fail to give any restriction on states. Nevertheless, the cross-simplicity can still be seen as implemented via suppression of intertwiner degrees of freedom in the dynamical propagation. In the second part of the paper, we investigate area spectra in the models. The results of these two investigations will highlight how, in the flipped model, the Hilbert space of states, as well as the spectra of area operators exactly match those of loop quantum gravity, whereas in the FKLS (and Barrett-Crane) models, the boundary Hilbert spaces and area spectra are different.Comment: 21 pages; statements about gamma limits made more precise, and minor phrasing change

Still on the way to quantizing gravity

I review and discuss some recent developments in non-perturbative approaches to quantum gravity, with an emphasis on discrete formulations, and those coming from a classical connection description.Comment: 15 pages, TeX; Invited talk at the 12th Italian Conference on General Relativity and Gravitational Physics, Roma, September 23-27, 199

The Vacuum State of Primordial Fluctuations in Hybrid Loop Quantum Cosmology

We investigate the role played by the vacuum of the primordial fluctuations in hybrid Loop Quantum Cosmology. We consider scenarios where the inflaton potential is a mass term and the unperturbed quantum geometry is governed by the effective dynamics of Loop Quantum Cosmology. In this situation, the phenomenologically interesting solutions have a preinflationary regime where the kinetic energy of the inflaton dominates over the potential. For these kind of solutions, we show that the primordial power spectra depend strongly on the choice of vacuum. We study in detail the case of adiabatic states of low order and the non-oscillating vacuum introduced by Mart\'in de Blas and Olmedo, all imposed at the bounce. The adiabatic spectra are typically suppressed at large scales, and display rapid oscillations with an increase of power at intermediate scales. In the non-oscillating vacuum, there is power suppression for large scales, but the rapid oscillations are absent. We argue that the oscillations are due to the imposition of initial adiabatic conditions in the region of kinetic dominance, and that they would also be present in General Relativity. Finally, we discuss the sensitivity of our results to changes of the initial time and other data of the model.Comment: 29 pages, 13 figure

Hawking emission from quantum gravity black holes

We address the issue of modelling quantum gravity effects in the evaporation of higher dimensional black holes in order to go beyond the usual semi-classical approximation. After reviewing the existing six families of quantum gravity corrected black hole geometries, we focus our work on non-commutative geometry inspired black holes, which encode model independent characteristics, are unaffected by the quantum back reaction and have an analytical form compact enough for numerical simulations. We consider the higher dimensional, spherically symmetric case and we proceed with a complete analysis of the brane/bulk emission for scalar fields. The key feature which makes the evaporation of non-commutative black holes so peculiar is the possibility of having a maximum temperature. Contrary to what happens with classical Schwarzschild black holes, the emission is dominated by low frequency field modes on the brane. This is a distinctive and potentially testable signature which might disclose further features about the nature of quantum gravity.Comment: 36 pages, 18 figures, v2: updated reference list, minor corrections, version matching that published on JHE