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Entropy of a Black Hole with Distinct Surface Gravities

Zhong Chao Wu
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Abstract

In gravitational thermodynamics, the entropy of a black hole with distinct surface gravities can be evaluated in a microcanonical ensemble. At the $WKB$ level, the entropy becomes the negative of the Euclidean action of the constrained instanton, which is the seed for the black hole creation in the no-boundary universe. Using the Gauss-Bonnet theorem, we prove the quite universal formula in Euclidean quantum gravity that the entropy of a nonrotating black hole is one quarter the sum of the products of the Euler characteristics and the areas of the horizons. For Lovelock gravity, the entropy and quantum creation of a black hole are also studied.

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Zhong Chao Wu. 1999-11-30. Entropy of a Black Hole with Distinct Surface Gravities. https://arxiv.org/abs/gr-qc/9911078

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