Black hole entropy and the dimensional continuation of the Gauss-Bonnet theorem

1993/09/25 by Máximo Bañados, Claudio Teitelboim, Jorge Zanelli · 247 citations
Physics and Astronomy · #Astrophysical Phenomena and Observations #Black Holes and Theoretical Physics #Black hole (networking) #Cosmology and Gravitation Theories #Einstein #Gauss–Bonnet theorem #Mathematical physics #Physics #gr-qc

paper · pdf · doi:10.1103/physrevlett.72.957

published in Physical Review Letters 72(7), 957-960 (American Physical Society) · 7 pages, RevTex

arxiv created 1993/09/25 · openalex publication_date 1994/02/14 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05

Abstract

The Euclidean black hole has topology gerR²\ifmmode×\else\texttimes\fiscrS^d\mathrm\ensuremath-2. It is shown that, in Einstein's theory the deficit angle of a cusp at any point in gerR² and the area of the scrS^d\mathrm\ensuremath-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 scrS^d\mathrm\ensuremath-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.

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