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On the topology and area of higher dimensional black holes

Mingliang Cai·Gregory J. Galloway
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Abstract

Over the past decade there has been an increasing interest in the study of black holes, and related objects, in higher (and lower) dimensions, motivated to a large extent by developments in string theory. The aim of the present paper is to obtain higher dimensional analogues of some well known results for black holes in 3+1 dimensions. More precisely, we obtain extensions to higher dimensions of Hawking's black hole topology theorem for asymptotically flat ($Λ=0$) black hole spacetimes, and Gibbons' and Woolgar's genus dependent, lower entropy bound for topological black holes in asymptotically locally anti-de Sitter ($Λ<0$) spacetimes. In higher dimensions the genus is replaced by the so-called $σ$-constant, or Yamabe invariant, which is a fundamental topological invariant of smooth compact manifolds.

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Mingliang Cai, Gregory J. Galloway. 2001-02-27. On the topology and area of higher dimensional black holes. https://doi.org/10.1088/0264-9381%2F18%2F14%2F308

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