Hamiltonian thermodynamics of a Lovelock black hole

TL;DR

This paper explores the Hamiltonian dynamics and thermodynamics of five-dimensional Lovelock black holes, revealing how their entropy and dominant solutions differ from Einstein's theory, especially at low temperatures.

Contribution

It introduces a canonical transformation simplifying the Lovelock theory and analyzes the thermodynamics, showing the robustness of Einstein black hole thermodynamics with Lovelock modifications.

Findings

Entropy follows the Lovelock Bekenstein-Hawking formula.

Low temperature limit yields a unique classical solution absent in Einstein theory.

Asymptotically flat space partition function does not exist.

Abstract

We consider the Hamiltonian dynamics and thermodynamics of spherically symmetric spacetimes within a one-parameter family of five-dimensional Lovelock theories. We adopt boundary conditions that make every classical solution part of a black hole exterior, with the spacelike hypersurfaces extending from the horizon bifurcation three-sphere to a timelike boundary with fixed intrinsic metric. The constraints are simplified by a Kucha\v{r}-type canonical transformation, and the theory is reduced to its true dynamical degrees of freedom. After quantization, the trace of the analytically continued Lorentzian time evolution operator is interpreted as the partition function of a thermodynamical canonical ensemble. Whenever the partition function is dominated by a Euclidean black hole solution, the entropy is given by the Lovelock analogue of the Bekenstein-Hawking entropy; in particular, in the low temperature 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 qualitative robustness of the thermodynamics of five-dimensional Einstein theory upon the addition of a nontrivial Lovelock term.