Entropy of black holes with arbitrary shapes in loop quantum gravity

Abstract

The quasi-local notion of an isolated horizon is employed to study the entropy of black holes without any particular symmetry in loop quantum gravity. The idea of characterizing the shape of a horizon by a sequence of local areas is successfully applied in the scheme to calculate the entropy by the $SO(1,1)$ BF boundary theory matching loop quantum gravity in the bulk. The generating function for calculating the microscopical degrees of freedom of a given isolated horizon is obtained. Numerical computations of small black holes indicate a new entropy formula containing the quantum correction related to the partition of the horizon. Further evidence shows that, for a given horizon area, the entropy decreases as a black hole deviates from the spherically symmetric one, and the entropy formula is also well suitable for big black holes.

9 pages, 2 figures, 2 tables

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• Shadow and stability of quantum-corrected black holes
• Loop quantum deparametrized Schwarzschild interior and discrete black hole mass
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• Axial gravitational quasinormal modes of a self-dual black hole in loop quantum gravity
• Shadows and optical appearance of quantum-corrected black holes illuminated by static thin accretions
• Spin foam amplitude of the black-to-white hole transition
• The thermodynamics of isolated horizons in loop quantum gravity
• Alternative $k=-1$ loop quantum cosmology