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On the Entropy of Quantum Fields in Black Hole Backgrounds

S. P. de Alwis·N. Ohta
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Abstract

We show that the partition function for a scalar field in a static spacetime background can be expressed as a functional integral in the corresponding optical space, and point out that the difference between this and the functional integral in the original metric is a Liouville type action. A general formula for the free energy is derived in the high temperature approximation and applied to various cases. In particular we find that thermodynamics in the extremal Reissner-Nordström space has extra singularities that make it ill-defined.

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S. P. de Alwis, N. Ohta. 1994-12-15. On the Entropy of Quantum Fields in Black Hole Backgrounds. https://arxiv.org/abs/hep-th/9412027

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