Black Hole Entropy and the Dimensional Continuation of the Gauss-Bonnet Theorem

Details Black Hole Entropy and the Dimensional Continuation of the Gauss-Bonnet Theorem Black Hole Entropy and the Dimensional Continuation of the Gauss-Bonnet Theorem

1993-09-25

arxiv.org/abs/gr-qc/9309026v1

Phys.Rev.Lett.72:957-960,1994

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

7 pages, RevTex

Scientific paper

10.1103/PhysRevLett.72.957

The Euclidean black hole has topology $\Re^2 \times {\cal S}^{d-2}$. It is shown that -in Einstein's theory- the deficit angle of a cusp at any point in $\Re^2$ and the area of the ${\cal S}^{d-2}$ are canonical conjugates. The black hole entropy emerges as the Euler class of a small disk centered at the horizon multiplied by the area of the ${\cal S}^{d-2}$ there.These results are obtained through dimensional continuation of the Gauss-Bonnet theorem. The extension to the most general action yielding second order field equations for the metric in any spacetime dimension is given.

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