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

Máximo Bañados·Claudio Teitelboim·Jorge Zanelli
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Abstract

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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Máximo Bañados, Claudio Teitelboim, Jorge Zanelli. 1993-09-25. Black Hole Entropy and the Dimensional Continuation of the Gauss-Bonnet Theorem. https://doi.org/10.1103/physrevlett.72.957

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