Geometric temperature and entropy of quantum isolated horizons

Abstract

By reintroducing Lorentz invariance in canonical loop quantum gravity, we define a geometrical notion of temperature for quantum isolated horizons. This is done by demanding that the horizon state satisfying the boundary conditions be a Kubo-Martin-Schwinger state. The exact formula for the temperature can be derived by imposing the reality conditions in the form of the linear simplicity constraints for an imaginary Barbero-Immirzi parameter. Thus, our analysis reveals the connection between the analytic continuation to the Ashtekar self-dual variables and the thermality of the horizon. The horizon thermal equilibrium state can then be used to compute both the entanglement and the Boltzmann entropies. We show that the two provide the same finite answer, which allows us to recover the Bekenstein-Hawking formula in the semi-classical limit. In this way, we shed new light on the microscopic origin of black hole entropy by revealing the equivalence between the near-horizon degrees of freedom entanglement proposal and the state-counting interpretation. The connection with the Connes-Rovelli thermal time proposal for a general relativistic statistical mechanics is worked out.

12 pages, 1 figure; v1 title: "Black hole entropy from KMS-states of quantum isolated horizons" changed in the editorial process; presentation improved in order to make it more self-contained and to clarify some important points. v2 matches the published version

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• Black Holes as Quantum Gravity Condensates
• Spherically symmetric sector of self dual Ashtekar gravity coupled to matter: Anomaly-free algebra of constraints with holonomy corrections
• Spacetime thermodynamics in the presence of torsion
• CFT/Gravity Correspondence on the Isolated Horizon
• An elementary introduction to loop quantum gravity
• Asymptotically de Sitter Universe inside a Schwarzschild black hole
• Covariance in self dual inhomogeneous models of effective quantum geometry: Spherical symmetry and Gowdy systems
• Horizon entropy with loop quantum gravity methods
• Testing the role of the Barbero-Immirzi parameter and the choice of connection in Loop Quantum Gravity
• Loop Quantum Cosmology with Complex Ashtekar Variables
• Statistical and entanglement entropy for black holes in quantum geometry
• Loop quantum cosmology with self-dual variables
• Spectra of geometric operators in three-dimensional LQG: From discrete to continuous
• Typicality in spin network states of quantum geometry
• Dynamical evaporation of quantum horizons
• A Note on Black Hole Entropy in Loop Quantum Gravity
• Anisotropic loop quantum cosmology with self-dual variables
• Immirzi parameter without Immirzi ambiguity: Conformal loop quantization of scalar-tensor gravity
• Gravity as an SU(1,1) gauge theory in four dimensions
• The Barbero-Immirzi Parameter: An Enigmatic Parameter of Loop Quantum Gravity
• Towards self dual Loop Quantum Gravity
• Orthogonal gauge fixing of first order gravity
• Semi-classical analysis of black holes in Loop Quantum Gravity: Modelling Hawking radiation with volume fluctuations
• Holographic bound in covariant loop quantum gravity
• A note on electrical and thermodynamic properties of Isolated Horizon
• Pure states statistical mechanics: On its foundations and applications to quantum gravity