Black Hole Entropy and the Dimensional Continuation of the Gauss-Bonnet Theorem
Preprint
- 25 September 1993
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.
Keywords
All Related Versions
- Version 1, 1993-09-25, ArXiv
- Published version: Physical Review Letters, 72 (7), 957.
This publication has 0 references indexed in Scilit: