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Entropy of black holes with arbitrary shapes in loop quantum gravity
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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.
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Image of a quantum-corrected black hole without Cauchy horizons illuminated by a static thin accretion disk
For the no-Cauchy-horizon quantum-corrected metric, a larger quantum parameter produces larger horizon, photon sphere, ISCO, and shadow, with narrower and tighter-spaced photon and lensed rings.
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