Reduction Arguments for Geometric Inequalities Associated With Asymptotically Hyperboloidal Slices

Abstract

We consider several geometric inequalities in general relativity involving mass, area, charge, and angular momentum for asymptotically hyperboloidal initial data. We show how to reduce each one to the known maximal (or time symmetric) case in the asymptotically flat setting, whenever a geometrically motivated system of elliptic equations admits a solution.

30 pages; final version

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Cited by in corpus (6)

• Geometrical inequalities bounding angular momentum and charges in General Relativity
• Spacetime Harmonic Functions and Applications to Mass
• The Jang equation and the positive mass theorem in the asymptotically hyperbolic setting
• The Conformal Flow of Metrics and the General Penrose Inequality
• Initial data sets with dominant energy condition admitting no smooth dec spacetime extension
• Asymptotically Hyperbolic Einstein Constraint Equations with Apparent Horizon Boundary and the Penrose Inequality for Perturbations of Schwarzschild-AdS