Astronomy and Astrophysics – Astrophysics – General Relativity and Quantum Cosmology
Scientific paper
1999-06-23
Class.Quant.Grav. 16 (1999) 3005-3012
Astronomy and Astrophysics
Astrophysics
General Relativity and Quantum Cosmology
Sign error in Equation (31) corrected, and minor notational correction. Footnote 2 removed because the paper it comments on ha
Scientific paper
10.1088/0264-9381/16/9/316
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 ${{4\pi (g-1)}\over {-\ell}}$ 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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