The Penrose inequality for perturbations of the Schwarzschild initial data

Abstract

We show that in the conformally flat case the Penrose inequality is satisfied for the Schwarzschild initial data with a small addition of the axially symmetric traceless exterior curvature. In this class the inequality is saturated only for data related to special sections of the Schwarzschild spacetime.

arXiv commentPaper accepted for publication in CQG

References in corpus (10)

• Solutions of the Einstein Constraint Equations with Apparent Horizon Boundaries
• The Penrose inequality and apparent horizons
• Constant mean curvature slices in the extended Schwarzschild solution and collapse of the lapse: Part I
• On the Penrose Inequality for general horizons
• Numerical Bifurcation Analysis of the Conformal Method
• Generalized Bowen--York Initial Data
• All transverse and TT tensors in flat spaces of any dimension
• Potentials for transverse trace-free tensors
• Coordinate independent expression for transverse trace-free tensors
• The general Penrose inequality: lessons from numerical evidence

Cited by in corpus (3)

• New spinorial mass-quasilocal angular momentum inequality for initial data with marginally future trapped surface
• Asymptotically Hyperbolic Einstein Constraint Equations with Apparent Horizon Boundary and the Penrose Inequality for Perturbations of Schwarzschild-AdS
• Recent Developments in the Penrose Conjecture