1999/06/30 by E. Woolgar, E Woolgar · 3 citations
Mathematics · Physics and Astronomy · #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #Geometric Analysis and Curvature Flows #astro-ph #gr-qc #hep-th
paper · pdf · doi:10.1088/0264-9381/16/9/316
published as Class.Quant.Grav. 16 (1999) 3005-3012 · Sign error in Equation (31) corrected, and minor notational correction. Footnote 2 removed because the paper it comments on has since been revised, making the footnote irrelevant. 16 pages, plain TeX, no figures
arxiv created 1999/07/08 · openalex publication_date 1999/08/06 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/30
By a simple modification of Hawking's well known topology theorems for black hole horizons, we find lower bounds for the areas of smooth apparent horizons and smooth cross sections of stationary black hole event horizons of genus g >1 in four dimensions. For a negatively curved Einstein space, the bound is 4 ( g -1)/(- ) where is the cosmological constant of the spacetime. This is complementary to the known upper bound on the area of g = 0 black holes in de Sitter spacetime. It also emerges that g >1 quite generally requires a mean negative energy density on the horizon. The bound is sharp; we show that it is saturated by certain extreme, asymptotically locally anti-de Sitter spacetimes. Our results generalize a recent result of Gibbons.