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Black-hole thermodynamics and Riemann surfaces. (English) Zbl 1029.83027
In this paper the author uses the analytic continuation procedure proposed in his earlier works [Adv. Theor. Math. Phys. 4, 929-979 (2000; Zbl 1011.81068) and Classical Quantum Gravity 19, 2399-2424 (2002; Zbl 1010.83040)] 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 of a black hole spacetime is a hyperbolic $$3$$-manifold having the topology of a handlebody. The boundary of this handlebody is a compact Riemann surface of genus $$G=2g+h-1$$.

##### MSC:
 83C57 Black holes 53B35 Local differential geometry of Hermitian and Kählerian structures 80A10 Classical and relativistic thermodynamics
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