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Journal Article

Black Hole Thermodynamics and Riemann Surfaces

MPS-Authors

Krasnov,  Kirill
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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50977.pdf
(Preprint), 197KB

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Citation

Krasnov, K. (2003). Black Hole Thermodynamics and Riemann Surfaces. Classical and Quantum Gravity, 20(11), 2235-2250.


Cite as: http://hdl.handle.net/11858/00-001M-0000-0013-521F-D
Abstract
We use the analytic continuation procedure proposed in our earlier works to study the thermodynamics of black holes in 2+1 dimensions. A general black hole in 2+1 dimensions has g handles hidden behind h horizons. The result of the analytic continuation is a hyperbolic 3-manifold having the topology of a handlebody. The boundary of this handlebody is a compact Riemann surface of genus G = 2g + h - 1. Conformal moduli of this surface encode in a simple way the physical characteristics of the black hole. The moduli space of black holes of a given type (g, h) is then the Schottky space at genus G. The (logarithm of the) thermodynamic partition function of the hole is the Kähler potential for the Weil-Peterson metric on the Schottky space. Bekenstein bound on the black hole entropy leads us to conjecture a new strong bound on this Kähler potential.