A Penrose inequality for graphs over Kottler space. (English) Zbl 1308.83093
Summary: In this work, we prove an optimal Penrose inequality for asymptotically locally hyperbolic manifolds which can be realized as graphs over Kottler space. Such inequality relies heavily on an optimal weighted Alexandrov-Fenchel inequality for the mean convex star-shaped hypersurfaces in Kottler space.
MSC:
| 83C57 | Black holes |
| 53C21 | Methods of global Riemannian geometry, including PDE methods; curvature restrictions |
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