Hamiltonian thermodynamics of the Reissner—Nordström—anti-de Sitter black hole

Jorma Louko and Stephen N. Winters-Hilt
Phys. Rev. D 54, 2647 – Published 15 August 1996
PDFExport Citation

Abstract

We consider the Hamiltonian dynamics and thermodynamics of spherically symmetric Einstein-Maxwell spacetimes with a negative cosmological constant. We impose boundary conditions that enforce every classical solution to be an exterior region of a Reissner—Nordström—anti-de Sitter black hole with a nondegenerate Killing horizon, with the spacelike hypersurfaces extending from the horizon bifurcation two-sphere to the asymptotically anti-de Sitter infinity. The constraints are simplified by a canonical transformation, which generalizes that given by Kuchař in the spherically symmetric vacuum Einstein theory, and the theory is reduced to its true dynamical degrees of freedom. After quantization, the grand partition function of a thermodynamical grand canonical ensemble is obtained by analytically continuing the Lorentzian time evolution operator to imaginary time and taking the trace. A similar analysis under slightly modified boundary conditions leads to the partition function of a thermodynamical canonical ensemble. The thermodynamics in each ensemble is analyzed, and the conditions that the (grand) partition function be dominated by a classical Euclidean black hole solution are found. When these conditions are satisfied, we recover, in particular, the Bekenstein-Hawking entropy. The limit of a vanishing cosmological constant is briefly discussed.

  • Received 2 February 1996

DOI:https://doi.org/10.1103/PhysRevD.54.2647

©1996 American Physical Society

Authors & Affiliations

Jorma Louko*,†

  • Department of Physics, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, Wisconsin 53201 and Department of Physics, University of Maryland, College Park, Maryland 20742-4111

Stephen N. Winters-Hilt

  • Department of Physics, University of Wisconsin-Milwaukee, P.O. Box 413, Milwaukee, Wisconsin 53201

  • *On leave of absence from Department of Physics, University of Helsinki. Electronic address: louko@wam.umd.edu
  • Present address.
  • Electronic address: winters@csd.uwm.edu

References (Subscription Required)

Click to Expand
Issue

Vol. 54, Iss. 4 — 15 August 1996

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review D

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×