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10 November 2024
 
  » arxiv » gr-qc/9309026

 Article overview



Black Hole Entropy and the Dimensional Continuation of the Gauss-Bonnet Theorem
Máximo Ba~nados ; Claudio Teitelboim ; Jorge Zanelli ;
Date 25 Sep 1993
Journal Phys.Rev.Lett. 72 (1994) 957-960
Subject gr-qc
AbstractThe Euclidean black hole has topology $Re^2 imes {cal S}^{d-2}$. 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.
Source arXiv, gr-qc/9309026
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