The Topological Origin of Black Hole Entropy

Details The Topological Origin of Black Hole Entropy The Topological Origin of Black Hole Entropy

2000-08-22

arxiv.org/abs/gr-qc/0008056v1

Int.J.Mod.Phys. D9 (2000) 711-716

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, received honorable mention from GRF2000

Scientific paper

In gravitational thermodynamics, the origin of a black hole's entropy is the topology of its instanton or constrained instanton. We prove that the entropy of an arbitrary nonrotating black hole is one quarter the sum of the products of the Euler characteristics of its horizons with their respective areas. The Gauss-Bonnet-like form of the action is not only crucial for the evaluation, but also for the existence of the entropy. This result covers all previous results on the entropy of a nonrotating black hole with a regular instanton. The argument can be readily extended into the lower or higher dimensional model. The problem of quantum creation of such a black hole is completely resolved.

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