HAMILTONIAN THERMODYNAMICS OF A LOVELOCK BLACK-HOLE

We consider the Hamiltonian dynamics and thermodynamics of spherically symmetric spacetimes within a one-parameter family of five-dimensiona l Lovelock theories. We adopt boundary conditions that make every clas sical solution part of a black hole exterior, with the spacelike hyper surfaces extending from the horizon bifurcation three-sphere to a time like boundary with fixed intrinsic metric. The constraints are simplif ied by a Kuchar-type canonical transformation, and the theory is reduc ed to its true dynamical degrees of freedom. After quantization, the t race of the analytically continued Lorentzian time evolution operator is interpreted as the partition function of a thermodynamical canonica l ensemble. Whenever the partition function is dominated by a Euclidea n black hole solution, the entropy is given by the Lovelock analogue o f the Bekenstein-Hawking entropy; in particular, in the low temperatur e limit the system exhibits a dominant classical solution that has no counterpart in Einstein's theory. The asymptotically flat space limit of the partition function does not exist. The results indicate qualita tive robustness of the thermodynamics of five-dimensional Einstein the ory upon the addition of a nontrivial Lovelock term.