The hyperbolic positive energy theorem

Abstract

We show that the causal-future-directed character of the energy-momentum vector of $n$-dimensional asymptotically hyperbolic Riemannian manifolds with spherical conformal infinity, $n\ge 3$, can be traced back to that of asymptotically Euclidean general-relativistic initial data sets satisfying the dominant energy condition.

minor corrections, to appear in JEMS

References in corpus (9)

• Rigidity and Positivity of Mass for Asymptotically Hyperbolic Manifolds
• The Higher Dimensional Positive Mass Theorem II
• Mass rigidity for hyperbolic manifolds
• Equality in the Spacetime Positive Mass Theorem
• The Trautman-Bondi mass of initial data sets
• Asymptotic gluing of asymptotically hyperbolic solutions to the Einstein constraint equations
• Energy in higher-dimensional spacetimes
• A density theorem for asymptotically hyperbolic initial data satisfying the dominant energy condition
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Cited by in corpus (10)

• Spacetime positive mass theorems for initial data sets with noncompact boundary
• On the stability of the positive mass theorem for asymptotically hyperbolic graphs
• On the energy of the Horowitz-Myers metrics
• Uniqueness and energy bounds for static AdS metrics
• The Jang equation and the positive mass theorem in the asymptotically hyperbolic setting
• Spacetime Harmonic Functions and Applications to Mass
• Dihedral rigidity of parabolic polyhedrons in hyperbolic spaces
• Positive mass theorems for asymptotically hyperbolic Riemannian manifolds with boundary
• The mass of an asymptotically hyperbolic end and distance estimates
• Hyperbolic positive energy theorems