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

Bañados, Máximo; Teitelboim, Claudio; Zanelli, Jorge

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

Authors

Bañados, Máximo

Teitelboim, Claudio

Zanelli, Jorge

Description

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.
7 pages, RevTex