Bounded Area Theorems for Higher Genus Black Holes

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 $\frac{4\pi (g-1)}{-\ell }$ 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.

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

Cited by in corpus (20)

• Gauss-Bonnet Black Holes in AdS Spaces
• Classification of near-horizon geometries of extremal black holes
• On the topology and area of higher dimensional black holes
• Towards the classification of static vacuum spacetimes with negative cosmological constant
• Ricci Flat Black Holes and Hawking-Page Phase Transition in Gauss-Bonnet Gravity and Dilaton Gravity
• New Five Dimensional Black Holes Classified by Horizon Geometry, and a Bianchi VI Braneworld
• New hairy black holes with negative cosmological constant
• A simple proof of the recent generalisations of Hawking's black hole topology theorem
• Geometrical inequalities bounding angular momentum and charges in General Relativity
• Bounds on area and charge for marginally trapped surfaces with cosmological constant
• Holographic Confinement/Deconfinement Phase Transitions of AdS/QCD in Curved Spaces
• Supersymmetric isolated horizons in ADS spacetime
• Some remarks on the size of bodies and black holes
• The kernel of the edth operators on higher-genus spacelike two-surfaces
• Non-existence of Asymptotically Flat Geons in 2+1 Gravity
• Uniqueness and energy bounds for static AdS metrics
• On the topology of untrapped surfaces
• The Smarr formula within the Geroch-Held-Penrose formalism
• Manifold invariants affect dynamics in ADS gravity
• Ultra-massive spacetimes in 2+1 dimensions with positive Λ