Almost Rigidity of the Positive Mass Theorem for Asymptotically Hyperbolic Manifolds with Spherical Symmetry

Abstract

We use the notion of intrinsic flat distance to address the almost rigidity of the positive mass theorem for asymptotically hyperbolic manifolds. In particular, we prove that a sequence of spherically symmetric asymptotically hyperbolic manifolds satisfying the conditions of the positive mass theorem converges to hyperbolic space in the intrinsic flat sense, if the limit of the mass along the sequence is zero.

23 pages, 1 figure. Minor typos corrected as requested by General Relativity and Gravitation when accepted for publication

References in corpus (3)

• Rigidity and Positivity of Mass for Asymptotically Hyperbolic Manifolds
• Stability of the positive mass theorem for graphical hypersurfaces of Euclidean space
• On the center of mass of asymptotically hyperbolic initial data sets

Cited by in corpus (6)

• Properties of the Null Distance and Spacetime Convergence
• Scalar and mean curvature comparison via the Dirac operator
• On the stability of the positive mass theorem for asymptotically hyperbolic graphs
• Stability of the Positive Mass Theorem and Riemannian Penrose Inequality for Asymptotically Hyperbolic Manifolds Foliated by Inverse Mean Curvature Flow
• Sobolev stability of the PMT and RPI using IMCF
• Asymptotically Hyperbolic 3-Metric with Ricci flow foliation