HAMILTONIAN THERMODYNAMICS OF 2-DIMENSIONAL VACUUM DILATONIC BLACK-HOLES

We consider the Hamiltonian dynamics and thermodynamics of the two-dim ensional vacuum dilatonic black hole in the presence of a timelike bou ndary with a fixed value of the dilaton field. A canonical transformat ion, previously developed by Varadarajan and Lau, allows a reduction o f the classical dynamics into an unconstrained Hamiltonian system with one canonical pair of degrees of freedom. The reduced theory is quant ized, and a partition function of a canonical ensemble is obtained as the trace of the analytically continued time evolution operator. The p artition function exists for any value of the dilaton field and of the temperature at the boundary, and the heat capacity is always positive . For temperatures higher than beta(c)(-1)=<(h)over bar lambda>/(2 pi) , the partition function is dominated by a classical black hole soluti on, and the dominant contribution to the entropy is the two-dimensiona l Bekenstein-Hawking entropy. For temperatures lower than beta(c)(-1), the partition function remains well behaved and the heat capacity is positive in the asymptotically hat space limit, in contrast with the c orresponding limit in four-dimensional spherically symmetric Einstein gravity; however, in this limit, the partition function is not dominat ed by a classical black hole solution.