Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields · 1995 · 167 citations · 23 references
Natural SciencesPhysicsGravitationMathematical PhysicsTheoretical PhysicsBlack HolesCurved SpacetimeGeneral RelativityGravitational FieldsQuantum Field TheoryQuantum GravityBlack Hole EntropyBlack Hole MetricsBlack Hole PhysicsBlack Hole SolutionsDifferential EntropyEvent Horizon In CosmologyEvent Horizon PhysicsKilling Vectors
ABSTRACT We consider the most general dilaton gravity theory in 1+1 dimensions. By suitably parametrizing the metric and scalar field we find a simple expression that relates the energy of a generic solution to the magnitude of the corresponding Killing vector. In theories that admit black hole solutions, this relationship leads directly to an expression for the entropy S=2\\pi \\tau_0/G, where \\tau_0 is the value of the scalar field (in this parametrization) at the event horizon. This result agrees with the one obtained using the more general method of Wald. Finally, we point out an intriguing connection between the black hole entropy and the imaginary part of the ``phase" of the exact Dirac quantum wave functionals for the theory.
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