Black hole entropy from the<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>S</mml:mi><mml:mi>U</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">)</mml:mo></mml:math>-invariant formulation of type I isolated horizons

Engle, Jonathan; Noui, Karim; Pérez, Alejandro; Pranzetti, Daniele

doi:10.1103/physrevd.82.044050

Cited by 143 publications

(343 citation statements)

References 48 publications

(67 reference statements)

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“…Specifically, Engle, Noui and Perez [19] have studied the problem from a purely SU(2) perspective, which more easily reveals the connection between loop quantum gravity and the boundary theory that it produces on the horizon. More details on their work is provided in [20]. In another series of interesting papers, by Basu, Kaul and Majumdar, they show that the U(1) formulation is equivalent to the SU(2) formulation subject to several natural constraints on the solder forms [21], [22].…”

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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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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“…In these work it is argued by means of an analytic continuation that the dimension of the Chern-Simons Hilbert space-used in modelling quantum isolated horizons [10,11]-grows exponentially with A/(4 2 p ) for large spin representations. A link between self-duality and thermal behaviour at Hawking temperature is also suggested by [12].…”

Section: Introductionmentioning

confidence: 99%

Statistics, holography, and black hole entropy in loop quantum gravity

2014

Self Cite

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In loop quantum gravity the quantum states of a black hole horizon are produced by point-like discrete quantum geometry excitations (or punctures) labelled by spin j. The excitations possibly carry other internal degrees of freedom also, and the associated quantum states are eigenstates of the area A operator. On the other hand, the appropriately scaled area operator A/(8π ) is also the physical Hamiltonian associated with the quasilocal stationary observers located at a small distance from the horizon. Thus, the local energy is entirely accounted for by the geometric operator A. We assume that:1. In a suitable vacuum state with regular energy momentum tensor at and close to the horizon the local temperature measured by stationary observers is the Unruh temperature and the degeneracy of 'matter' states is exponential with the area exp (λA/ 2 p )-this is supported by the well established results of QFT in curved spacetimes, which do not determine λ but asserts an exponential behaviour.2. The geometric excitations of the horizon (punctures) are indistinguishable.3. In the semiclassical limit the area of the black hole horizon is large in Planck units. It follows that:1. Up to quantum corrections, matter degrees of freedom saturate the holographic bound, viz.λ must be equal to 1 4 .2. Up to quantum corrections, the statistical black hole entropy coincides with Bekenstein-3. The number of horizon punctures goes like N ∝ A/ 2 p , i.e. the number of punctures N remains large in the semiclassical limit. We also show how the present model (constructed from loop quantum gravity) provides a regularization of (and gives a concrete meaning to) the formal Gibbons-Hawking euclidean path-integral 2 treatment of the black hole system. These results offer a new scenario for semiclassical consistency of loop quantum gravity in the context of black hole physics, and suggest a concrete dynamical mechanism for large spin domination leading simultaneously to semiclassicality and continuity.

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“…This has an obvious importance for quantization as constraints must be incorporated in one way or another. Numerous investigations about this problem have appeared in the literature; see for example [1][2][3][4][5][6][7][8][9][10] and references therein. Some of these works, in particular those devoted to study the integrability (existence and uniqueness problems) of the Yang-Mills equations in bounded domains, take into consideration the relevant functional analytic issues [7,8].…”

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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Black hole entropy from theSU(2)-invariant formulation of type I isolated horizons

Cited by 143 publications

References 48 publications

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

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

Statistics, holography, and black hole entropy in loop quantum gravity

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

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