Hamiltonian thermodynamics of 2D vacuum dilatonic black holes

We consider the Hamiltonian dynamics and thermodynamics of the twodimensional vacuum dilatonic black hole in the presence of a timelike boundary with a fixed value of the dilaton field. A canonical transformation, previously developed by Varadarajan and Lau, allows a reduction of the classical dynamics into an unconstrained Hamiltonian system with one canonical pair of degrees of freedom. The reduced theory is quantized, and a partition function of a canonical ensemble is obtained as the trace of the analytically continued time evolution operator. The partition function exists for any values of the dilaton field and the temperature at the boundary, and the heat Electronic address: [email protected] Electronic address: [email protected]. On leave of absence from Department of Physics, University of Helsinki. Electronic address: [email protected] Electronic address: [email protected] 1 capacity is always positive. For temperatures higher than β−1 c = h̄λ/(2π), the partition function is dominated by a classical black hole solution, and the dominant contribution to the entropy is the two-dimensional BekensteinHawking entropy. For temperatures lower than β−1 c , the partition function remains well-behaved and the heat capacity is positive in the asymptotically flat space limit, in contrast to the corresponding limit in four-dimensional spherically symmetric Einstein gravity; however, in this limit, the partition function is not dominated by a classical black hole solution. Pacs: 04.70.Dy, 04.60.Ds, 04.60.Kz, 04.20.Fy Typeset using REVTEX 2