Hamiltonian thermodynamics of two-dimensional vacuum dilatonic black holes

Abstract

We consider the Hamiltonian dynamics and thermodynamics of the two-dimensional 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 capacity is always positive. For temperatures higher than ${\beta }_c^{-1}=\hslash \lambda /(2\pi )$, the partition function is dominated by a classical black hole solution, and the dominant contribution to the entropy is the two-dimensional 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 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.

20 pages, REVTEX. Added a discussion on the boundary action and boundary terms in Sec. IIIA. Minor changes in Acknowledgements and References

References in corpus (17)

• On Geometric Entropy
• Black Hole Entropy in Canonical Quantum Gravity and Superstring Theory
• Geometrodynamics of Schwarzschild Black Holes
• The Statistical Mechanics of the (2+1)-Dimensional Black Hole
• Black hole thermodynamics and information loss in two dimensions
• Aspects of Black Hole Quantum Mechanics and Thermodynamics in 2+1 Dimensions
• Black Hole Entropy in Two Dimensions
• Semi-infinite Throat as the End-state Geometry of two-dimensional Black Hole Evaporation
• Hamiltonian thermodynamics of the Schwarzschild black hole
• Black Holes as Quantum Membranes
• Why the Entropy of a Black Hole is $A/4$?
• Two-dimensional Quantum-Corrected Eternal Black Hole
• On the Canonical Reduction of Spherically Symmetric Gravity
• Hawking Radiation and Unitary evolution
• Entropy and black hole horizons
• Evaporating Black Holes and Entropy
• Classical and quantum geometrodynamics of 2d vacuum dilatonic black holes

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