Detailed black hole state counting in loop quantum gravity

Agulló, Iván; Borja, Enrique F.; Diaz-Polo, Jacobo; Villaseñor, Eduardo J. S.

doi:10.1103/physrevd.82.084029

Cited by 91 publications

(122 citation statements)

References 43 publications

(143 reference statements)

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“…In this paper we study the finite k counting problem by means of simple asymptotic methods. The powerful methods that have been developed for the resolution of the counting problem in the k = ∞ [18][19][20][21][22][23][24] are perhaps generalizable to the finite k case. Here we follow a less rigorous and more physical approach.…”

Section: Jhep05(2011)016mentioning

confidence: 99%

“…We adapt the techniques used in [18][19][20][21][22] and firstly introduced in [11,12] to compute the entropy of a black hole. We are not going into the mathematical details of these techniques which has been very well exposed in [18][19][20][21][22] and which are in fact very well-known in the domain of probabilities and used to understand some properties of random walks. We recover that in the spherically symmetric and distorted black holes, the leading term of the entropy is proportional to the area and the first corrections are still logarithmic: S(a) ∼ αa + β log a.…”

Section: Jhep05(2011)016mentioning

confidence: 99%

“…In this case it is natural (although not necessary) to consider SU(2) (or U(1)) Chern-Simons theory with a level that scales with the macroscopic classical area k ∝ a H . This makes the state-counting (necessary for the computation of the entropy) a combinatorial problem which can be entirely formulated in terms of the representation theory of the classical group SU(2) (or U(1)): for practical purposes one can take k = ∞ from the starting point [11][12][13][14][15][16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

The SU(2) black hole entropy revisited

Engle

Noui

Pérez

et al. 2011

J. High Energ. Phys.

106

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Abstract:We study the state-counting problem that arises in the SU(2) black hole entropy calculation in loop quantum gravity. More precisely, we compute the leading term and the logarithmic correction of both the spherically symmetric and the distorted SU(2) black holes. Contrary to what has been done in previous works, we have to take into account "quantum corrections" in our framework in the sense that the level k of the Chern-Simons theory which describes the black hole is finite and not sent to infinity. Therefore, the new results presented here allow for the computation of the entropy in models where the quantum group corrections are important.

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Section: Jhep05(2011)016mentioning

confidence: 99%

Section: Jhep05(2011)016mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

The SU(2) black hole entropy revisited

Engle

Noui

Pérez

et al. 2011

J. High Energ. Phys.

106

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show abstract

“…Since γ plays a pivotal role in the theory, determining its value is of great importance. It should be noted that even with the γ ambiguity, careful calculations have shown that the entropy using this technique is indeed linearly proportional to the area of the black hole [5], [6], [7], [8]. The degeneracy spectrum of black holes and its relation to the entropy has also recently been studied in [9].…”

Section: Introductionmentioning

confidence: 99%

A note on the symmetry reduction of SU(2) on horizons of various topologies

DeBenedictis¹,

Kloster²,

Brännlund³

2011

Class. Quantum Grav.

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It is known that the SU(2) degrees of freedom manifest in the description of the gravitational field in loop quantum gravity are generally reduced to U(1) degrees of freedom on an S 2 isolated horizon. General relativity also allows black holes with planar, toroidal, or higher genus topology for their horizons. These solutions also meet the criteria for an isolated horizon, save for the topological criterion, which is not crucial. We discuss the relevant corresponding symmetry reduction for black holes of various topologies (genus 0 and ≥ 2) here and discuss its ramifications to black hole entropy within the loop quantum gravity paradigm. Quantities relevant to the horizon theory are calculated explicitly using a generalized ansatz for the connection and densitized triad as well as utilizing a general metric admitting hyperbolic sub-spaces. In all scenarios, the internal symmetry may be reduced to combinations of U(1).

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“…We summarize two of these -the simple argument of Rovelli's [41] and the number theoretical approach of [42,43].…”

Section: Black Hole Entropymentioning

confidence: 99%

LQG for the Bewildered

Bilson-Thompson

Vaid

2017

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We present a pedagogical introduction to the notions underlying the connection formulation of General Relativity -Loop Quantum Gravity (LQG) -with an emphasis on the physical aspects of the framework. We begin by reviewing General Relativity and Quantum Field Theory, to emphasise the similarities between them which establish a foundation upon which to build a theory of quantum gravity. We then explain, in a concise and clear manner, the steps leading from the Einstein-Hilbert action for gravity to the construction of the quantum states of geometry, known as spin-networks, which provide the basis for the kinematical Hilbert space of quantum general relativity. Along the way we introduce the various associated concepts of tetrads, spin-connection and holonomies which are a pre-requisite for understanding the LQG formalism. Having provided a minimal introduction to the LQG framework, we discuss its applications to the problems of black hole entropy and of quantum cosmology. A list of the most common criticisms of LQG is presented, which are then tackled one by one in order to convince the reader of the physical viability of the theory.An extensive set of appendices provide accessible introductions to several key notions such as the Peter-Weyl theorem, duality of differential forms and Regge calculus, among others. The presentation is aimed at graduate students and researchers who have some familiarity with the tools of quantum mechanics and field theory and/or General Relativity, but are intimidated by the seeming technical prowess required to browse through the existing LQG literature. Our hope is to make the formalism appear a little less bewildering to the un-initiated and to help lower the barrier for entry into the field.

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Detailed black hole state counting in loop quantum gravity

Cited by 91 publications

References 43 publications

The SU(2) black hole entropy revisited

The SU(2) black hole entropy revisited

A note on the symmetry reduction of SU(2) on horizons of various topologies

LQG for the Bewildered

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