A Gibbons-Penrose inequality for surfaces in Schwarzschild spacetime

Abstract

We propose a geometric inequality for two-dimensional spacelike surfaces in the Schwarzschild spacetime. This inequality implies the Penrose inequality for collapsing dust shells in general relativity, as proposed by Penrose and Gibbons. We prove that the inequality holds in several important cases.

11 pages. Final version. To appear in Communications in Mathematical Physics

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• Quasilocal mass in general relativity
• Isometric embeddings into the Minkowski space and new quasi-local mass
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• A Minkowski inequality for hypersurfaces in the Anti-deSitter-Schwarzschild manifold
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• Inverse curvature flow in anti-de Sitter-Schwarzschild manifold
• Minkowski formulae and Alexandrov theorems in spacetime
• Inverse anisotropic mean curvature flow and a Minkowski type inequality