9 research outputs found
Entropy in the Classical and Quantum Polymer Black Hole Models
We investigate the entropy counting for black hole horizons in loop quantum
gravity (LQG). We argue that the space of 3d closed polyhedra is the classical
counterpart of the space of SU(2) intertwiners at the quantum level. Then
computing the entropy for the boundary horizon amounts to calculating the
density of polyhedra or the number of intertwiners at fixed total area.
Following the previous work arXiv:1011.5628, we dub these the classical and
quantum polymer models for isolated horizons in LQG. We provide exact
micro-canonical calculations for both models and we show that the classical
counting of polyhedra accounts for most of the features of the intertwiner
counting (leading order entropy and log-correction), thus providing us with a
simpler model to further investigate correlations and dynamics. To illustrate
this, we also produce an exact formula for the dimension of the intertwiner
space as a density of "almost-closed polyhedra".Comment: 24 page
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
Modelling black holes with angular momentum in loop quantum gravity
We construct a SU(2) connection formulation of Kerr isolated horizons. As in the non-rotating case, the model is based on a SU(2) Chern\u2013Simons theory describing the degrees of freedom on the horizon. The presence of a non-vanishing angular momentum modifies the admissibility conditions for spin network states. Physical states of the system are in correspondence with open intertwiners with total spin matching the angular momentum of the spacetime. \ua9 2014, Springer Science+Business Media New York
Dynamical evaporation of quantum horizons
We describe the black hole evaporation process driven by the dynamical evolution of the quantum gravitational degrees of freedom resident at the horizon, as identified by the loop quantum gravity kinematics. Using a parallel with the Brownian motion, we interpret the first law of quantum dynamical horizon in terms of a fluctuation-dissipation relation. In this way, the horizon evolution is described in terms of relaxation to an equilibrium state balanced by the excitation of Planck scale constituents of the horizon. This discrete quantum hair structure associated to the horizon geometry produces a deviation from thermality in the radiation spectrum. We investigate the final stage of the evaporation process and show how the dynamics leads to the formation of a massive remnant, which can eventually decay. Implications for the information paradox are discussed