Quantum geometry of isolated horizons and black hole entropy

By Abhay Ashtekar, John C. Baez, K. Krasnov. 2000

546 citations recorded by the source corpus.

Using the earlier developed classical Hamiltonian framework as the point of departure, we carry out a non-perturbative quantization of the sector of general relativity, coupled to matter, admitting non-rotating isolated horizons as inner boundaries. The emphasis is on the quantum geometry of the horizon. Polymer excitations of the bulk quantum geometry pierce the horizon endowing it with area. The intrinsic geometry of the horizon is then described by the quantum Chern-Simons theory of a U(1) connection on a punctured 2-sphere, the horizon. Subtle mathematical features of the quantum Chern-Simons theory turn out to be important for the existence of a coherent quantum theory of the horizon geometry. Heuristically, the intrinsic geometry is flat everywhere except at the punctures. The distributional curvature of the U(1) connection at the punctures gives rise to quantized deficit angles which account for the overall curvature. For macroscopic black holes, the logarithm of the number of these horizon microstates is proportional to the area, irrespective of the values of (non-gravitational) charges. Thus, the black hole entropy can be accounted for entirely by the quantum states of the horizon geometry. Our analysis is applicable to all non-rotating black holes, including the astrophysically interesting ones which are very far from extremality. Furthermore, cosmological horizons (to which statistical mechanical considerations are known to apply) are naturally incorporated. An effort has been made to make the paper self-contained by including short reviews of the background material.

Subfields: Astronomy and Astrophysics, Nuclear and High Energy Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0aadaa53f13c4b760fd2b2cc502e438445037ac3

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Citations in the corpus

The Spin-Foam Approach to Quantum Gravity (2012, background): “The computation of black-hole entropy in LQG fixes the value of γ (see [26]).”
Introduction to loop quantum gravity and spin foams (2004, unknown): “) Cyl as follows. Given a cylindrical function ψγ,f[A] ∈ Cyl (as in Introduction to Loop Quantum Gravity and Spin Foams 25 (73)) µAL(ψγ,f) is deﬁned as µAL(ψγ,f) = Z Y e⊂γ dhe f(he 1,he 2,···heN e ), (80) where he ∈ SU(2) and dhis the (normalized) Haar measure of SU(2) l. The measure µAL is clearly ”
Loop Quantum Gravity (2003, background): “See the standard reference [137] or a recent review such as [138] for a detailed calculation and more complete references.”
On the classification of asymptotic quasinormal frequencies for $d$-dimensional black holes and quantum gravity (2004, methodology): “where there are N punctures at the event horizon and where jp labels the SU(2) representation associated to the spin network edge piercing at puncture p (see [81] for further details).”
Loop quantum gravity: an outside view (2005, methodology): “The explanation of the Bekenstein–Hawking entropy of black holes [45, 46] in terms of microstates has been claimed as a success for both LQG [47, 48] and string theory [49].”
Gravity and the thermodynamics of horizons (2005, background): “given horizon area and estimate the entropy. One gets the correct numerical factor (only) if γ= lnm/2π √ 2 where m= 2 or m= 3 depending on whether the gauge group SU(2) or SO(3) is used in the theory [128,129,130,131]. Again there are several unresolved issues. To begin with, it is not clear how exa”
Quantum gravity with a positive cosmological constant (2002, background): “• There is a natural boundary term[13] which may be added to study the case of horizons[14, 15 ] or timelike boundaries[16, 17].”
Quantum nature of the big bang: An analytical and numerical investigation (2006, background): “A broad answer —illustrated by the area eigenvalues of isolated horizons [59, 60]— is that the discreteness will generically descend to the physical sector at least in cases where one can construct Dirac observables directly from the kinematical geometrical operators [1].”
Loop Quantum Cosmology (2005, background): “The spectrum depends on the value of the Barbero–Immirzi parameter, which can accordingly be fixed using implications of the spectrum such as black hole entropy, which gives a value of the order of but smaller than one [11, 12, 108, 155].”