Black hole entropy and the dimensional continuation of the Gauss-Bonnet theorem
Black hole entropy and the dimensional continuation of the Gauss-Bonnet theorem
The Euclidean black hole has topology ${\mathit{gerR}}^{2}$\ifmmode\times\else\texttimes\fi{}${\mathit{scrS}}^{\mathit{d}\mathrm{\ensuremath{-}}2}$. It is shown that, in Einstein's theory the deficit angle of a cusp at any point in ${\mathit{gerR}}^{2}$ and the area of the ${\mathit{scrS}}^{\mathit{d}\mathrm{\ensuremath{-}}2}$ are canonical conjugates. The black hole entropy emerges as the Euler class of a small disk centered at the …