On perturbations of the Schwarzschild anti-de Sitter spaces of positive mass

Abstract

In this paper we prove the Penrose inequality for metrics that are small perturbations of the Schwarzschild anti-de Sitter metrics of positive mass. We use the existence of a global foliation by weakly stable constant mean curvature spheres and the monotonicity of the Hawking mass.

19 pages. Revised version. To appear in Communications in Mathematical Physics

References in corpus (2)

• Present status of the Penrose inequality
• A volume comparison theorem for asymptotically hyperbolic manifolds

Cited by in corpus (4)

• Large isoperimetric regions in asymptotically hyperbolic manifolds
• Constructing electrically charged Riemannian manifolds with minimal boundary, prescribed asymptotics, and controlled mass
• The Penrose inequality in spherical symmetry with charge and in Gauss-Bonnet gravity
• Asymptotically Hyperbolic Einstein Constraint Equations with Apparent Horizon Boundary and the Penrose Inequality for Perturbations of Schwarzschild-AdS