Abstract
The Euclidean black hole has topology ×. It is shown that, in Einstein’s theory the deficit angle of a cusp at any point in and the area of the 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 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.
- Received 27 September 1993
DOI:https://doi.org/10.1103/PhysRevLett.72.957
©1994 American Physical Society