Black Hole State Counting in Loop Quantum Gravity: A Number-Theoretical Approach

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

doi:10.1103/physrevlett.100.211301

Cited by 109 publications

(195 citation statements)

References 15 publications

(45 reference statements)

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“…The microscopic behavior of the exact quantum entropy S bh is reminiscent of the substructure found in [17,18] for the entropy of black holes when the standard form of the area spectrum is considered. The even areas a 2u are responsible for the large scale properties of the entropy, for the value of given by (6.3), and the logarithmic correction to the entropy with the usual À1=2 coefficient.…”

Section: The Relevance Of the Even And Odd Sectorsmentioning

confidence: 89%

Flux-area operator and black hole entropy

Lewandowski

Villaseñor

2009

Phys. Rev. D

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We show that, for space-times with inner boundaries, there exists a natural area operator different from the standard one used in loop quantum gravity. This new flux-area operator has equidistant eigenvalues. We discuss the consequences of substituting the standard area operator in the Ashtekar-Baez-CorichiKrasnov definition of black hole entropy by the new one. Our choice simplifies the definition of the entropy and allows us to consider only those areas that coincide with the one defined by the value of the level of the Chern-Simons theory describing the horizon degrees of freedom. We give a prescription to count the number of relevant horizon states by using spin components and obtain exact expressions for the black hole entropy. Finally we derive its asymptotic behavior, discuss several issues related to the compatibility of our results with the Bekenstein-Hawking area law and the relation with Schwarzschild quasinormal modes.

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Section: The Relevance Of the Even And Odd Sectorsmentioning

confidence: 89%

Flux-area operator and black hole entropy

Lewandowski

Villaseñor

2009

Phys. Rev. D

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“…13 This fact is more than a useful analogy because it is possible to introduce and study an abstract wave equation that encompasses many relevant linear models [20]. This means that in addition to having the possibility of considering many different kinds of fields (scalar or vector fields, for instance) we can also discuss, in the same setting, all the different boundary conditions that they must satisfy.…”

Section: Appendix A: Functional Spaces Used In the Paper: A Compilatimentioning

confidence: 99%

“…For example, the holo-graphic models, where they are associated with hypersurfaces (or boundaries) of spacetime, come immediately to mind. Another interesting example is provided by quantum black hole models, in particular those that make use of inner boundaries for their description [12][13][14]. A precise determination and understanding of the quantum states requires the obtention of the independent classical configurations of the system, i.e.…”

Section: Introductionmentioning

confidence: 99%

Hamiltonian treatment of linear field theories in the presence of boundaries: a geometric approach

Prieto

Villaseñor

2014

Class. Quantum Grav.

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The purpose of this paper is to study in detail the constraint structure of the Hamiltonian and symplectic-Lagrangian descriptions for the scalar and electromagnetic fields in the presence of spatial boundaries. We carefully discuss the implementation of the geometric constraint algorithm of Gotay, Nester and Hinds with special emphasis on the relevant functional analytic aspects of the problem. This is an important step towards the rigorous understanding of general field theories in the presence of boundaries, very especially when these fail to be regular. The geometric approach developed in the paper is also useful with regard to the interpretation of the physical degrees of freedom and the nature of the constraints when both gauge symmetries and boundaries are present.

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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%

“…As shown in [42] this problem can be mapped to a non-interacting spin-system [46] as follows. Consider a chain of N spins each of which can be in an up | ↑ state or a down | ↓ state.…”

Section: Number Theoretical Approachmentioning

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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Black Hole State Counting in Loop Quantum Gravity: A Number-Theoretical Approach

Cited by 109 publications

References 15 publications

Flux-area operator and black hole entropy

Flux-area operator and black hole entropy

Hamiltonian treatment of linear field theories in the presence of boundaries: a geometric approach

LQG for the Bewildered

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