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Bounded Area Theorems for Higher Genus Black Holes

E. Woolgar
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Abstract

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 ${{4π(g-1)}\over {-\ell}}$ where $\ell$ 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.

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BibTeXRIS

E. Woolgar. 1999-07-08. Bounded Area Theorems for Higher Genus Black Holes. https://doi.org/10.1088/0264-9381%2F16%2F9%2F316

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