Action and entropy of black holes in spacetimes with a cosmological constant

Details Action and entropy of black holes in spacetimes with a cosmological constant Action and entropy of black holes in spacetimes with a cosmological constant

1997-08-26

arxiv.org/abs/gr-qc/9708062v2

Class.Quant.Grav.15:2783-2793,1998

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Revtex, 13 pages, no figures

Scientific paper

10.1088/0264-9381/15/9/023

In the Euclidean path integral approach, we calculate the actions and the entropies for the Reissner-Nordstr\"om-de Sitter solutions. When the temperatures of black hole and cosmological horizons are equal, the entropy is the sum of one-quarter areas of black hole and cosmological horizons; when the inner and outer black hole horizons coincide, the entropy is only one-quarter area of cosmological horizon; and the entropy vanishes when the two black hole horizons and cosmological horizon coincide. We also calculate the Euler numbers of the corresponding Euclidean manifolds, and discuss the relationship between the entropy of instanton and the Euler number.

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