Initial data rigidity results

Abstract

We present several rigidity results for initial data sets motivated by the positive mass theorem. An important step in our proofs here is to establish conditions that ensure that a marginally outer trapped surface is "weakly outermost". A rigidity result for Riemannian manifolds with a lower bound on their scalar curvature is included as a special case.

arXiv comment22 pages. Final version. Published in Commun. Math. Phys., vol. 386 (2021). All comments welcome

References in corpus (10)

• Local existence of dynamical and trapping horizons
• A generalization of Hawking's black hole topology theorem to higher dimensions
• Rigidity and Positivity of Mass for Asymptotically Hyperbolic Manifolds
• The area of horizons and the trapped region
• The Higher Dimensional Positive Mass Theorem II
• Equality in the Spacetime Positive Mass Theorem
• Existence, Regularity, and Properties of Generalized Apparent Horizons
• Rigidity of outermost MOTS - the initial data version
• Positive Scalar Curvature and Minimal Hypersurface Singularities
• Some remarks on the size of bodies and black holes

Cited by in corpus (7)

• Positive mass theorems for asymptotically hyperbolic Riemannian manifolds with boundary
• Dihedral rigidity for cubic initial data sets
• Doubling of asymptotically flat half-spaces and the Riemannian Penrose inequality
• Rigidity aspects of Penrose's singularity theorem
• The Positive Energy Theorem for Asymptotically Hyperboloidal Initial Data Sets With Toroidal Infinity and Related Rigidity Results
• Hyperbolic positive energy theorems
• Rigidity results for initial data sets satisfying the dominant energy condition