Asymptotically Hyperbolic Einstein Constraint Equations with Apparent Horizon Boundary and the Penrose Inequality for Perturbations of Schwarzschild-AdS

Abstract

We prove the existence of asymptotically hyperbolic solutions to the vacuum Einstein constraint equations with a marginally outer trapped boundary of positive mean curvature, using the constant mean curvature conformal method. As an application of this result, we verify the Penrose inequality for certain perturbations of Schwarzschild Anti-de Sitter black hole initial data.

24 pages

References in corpus (6)

• The area of horizons and the trapped region
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• On the Penrose inequality in anti-deSitter space
• Non-CMC Solutions to the Einstein Constraint Equations on Asymptotically Euclidean Manifolds with Apparent Horizon Boundaries
• The Penrose inequality for perturbations of the Schwarzschild initial data
• Sobolev-class asymptotically hyperbolic manifolds and the Yamabe problem