2001/02/27 by Mingliang Cai, Gregory J. Galloway · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Geometric Analysis and Curvature Flows #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/18/14/308
published as Class.Quant.Grav. 18 (2001) 2707-2718 · 15 pages, Latex2e; typos corrected, a convention clarified, resulting in the simplification of certain formulas, other improvements
arxiv created 2001/02/27 · openalex publication_date 2001/06/29 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/30
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.