Results 1 
8 of
8
2007 Renormalization and black hole entropy in loop quantum gravity Class
 Quantum Grav
"... Microscopic state counting for a black hole in Loop Quantum Gravity yields a result proportional to horizon area, and inversely proportional to Newton’s constant and the Immirzi parameter. It is argued here that before this result can be compared to the BekensteinHawking entropy of a macroscopic bl ..."
Abstract

Cited by 13 (0 self)
 Add to MetaCart
(Show Context)
Microscopic state counting for a black hole in Loop Quantum Gravity yields a result proportional to horizon area, and inversely proportional to Newton’s constant and the Immirzi parameter. It is argued here that before this result can be compared to the BekensteinHawking entropy of a macroscopic black hole, the scale dependence of both Newton’s constant and the area must be accounted for. The two entropies could then agree for any value of the Immirzi parameter, if a certain renormalization property holds. The number of microscopic states of a black hole has been computed in Loop Quantum Gravity (LQG), in the state space of spin networks. The result for the entropy of a black hole with horizon area A is SLQG = b A, (1) γ �G where b is a numerical constant and γ is the Immirzi parameter. These calculations have a long and continuing history (see for example [1, 2, 3, 4, 5, 6, 7, 8] and for reviews [9, 10, 11]), including some controversy over the correct evaluation of the number of states. The results differ only in the value of b however (unless states related by surface diffeomorphisms are identified, as has discussed for example in [12]). In addition to the case of spherically symmetric, static black holes, the result (1) has been shown to hold, with the same value of b, in the presence of scalar, Maxwell, and YangMills fields [13] 1
GRAVITATIONAL STATISTICAL MECHANICS: A MODEL
, 2001
"... Using the quantum Hamiltonian for a gravitational system with boundary, we find the partition function and derive the resulting thermodynamics. The Hamiltonian, and starting point for this calculation, is the boundary term required by functional differentiability of the action for Lorentzian gener ..."
Abstract
 Add to MetaCart
Using the quantum Hamiltonian for a gravitational system with boundary, we find the partition function and derive the resulting thermodynamics. The Hamiltonian, and starting point for this calculation, is the boundary term required by functional differentiability of the action for Lorentzian general relativity. In this model, states of quantum geometry are represented by spin networks. We show that the statistical mechanics of the model reduces to a simple noninteracting gas of particles with spin. Using both canonical and grand canonical descriptions, we investigate two temperature regimes determined by the fundamental constant in the theory, m. In the high temperature limit (T ≫ m), the model is thermodynamically stable. For low temperatures (T ≪ m) and for macroscopic areas of the bounding surface, the entropy is proportional to area (with logarithmic correction), providing a simple derivation of the BekensteinHawking result. The system obeys a first law. By comparing our results to known semiclassical relations we are able to fix the fundamental scale m. Also in the low temperature, macroscopic limit, the quantum geometry on the boundary forms a ‘condensate’ in the lowest level (j = 1/2).
BarberoImmirzi parameter in Regge calculus
, 804
"... We consider Regge calculus in the representation in terms of area tensors and self and antiselfdual connections generalised to the case of Holst action that is standard Einstein action in the tetradconnection variables plus topological (on equations of motion for connections) term with coefficient ..."
Abstract
 Add to MetaCart
(Show Context)
We consider Regge calculus in the representation in terms of area tensors and self and antiselfdual connections generalised to the case of Holst action that is standard Einstein action in the tetradconnection variables plus topological (on equations of motion for connections) term with coefficient 1/γ, γ known as BarberoImmirzi parameter. The quantum measure is shown to exponentially fall off with areas with typical cutoff scales 2πG and 2πGγ in spacelike and timelike regions, respectively (G is the Newton constant). PACS numbers: 04.60.m Quantum gravity2 The formal nonrenormalisability of quantum version of general relativity (GR) may cause us to try to find alternatives to the continuum description of underlying spacetime structure. An example of such the alternative description may be given by Regge calculus (RC) suggested in 1961 [1]. It is the exact GR developed in the piecewise flat spacetime which is a particular case of general Riemannian spacetime [2]. In turn, the general Riemannian spacetime can be considered as limiting case of the piecewise flat
Black Hole Thermodynamics
"... Abstract The discovery in the early 1970s that black holes radiate as black bodies has radically affected our understanding of general relativity, and offered us some early hints about the nature of quantum gravity. In this chapter I will review the discovery of black hole thermodynamics and summar ..."
Abstract
 Add to MetaCart
(Show Context)
Abstract The discovery in the early 1970s that black holes radiate as black bodies has radically affected our understanding of general relativity, and offered us some early hints about the nature of quantum gravity. In this chapter I will review the discovery of black hole thermodynamics and summarize the many independent ways of obtaining the thermodynamic and (perhaps) statistical mechanical properties of black holes. I will then describe some of the remaining puzzles, including the nature of the quantum microstates, the problem of universality, and the information loss paradox. *