On the topology and area of higher-dimensional black holes

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88 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)2707-2718
Number of pages12
JournalClassical and Quantum Gravity
Issue number14
StatePublished - Jul 21 2001

ASJC Scopus subject areas

  • Physics and Astronomy (miscellaneous)

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