A density theorem for asymptotically hyperbolic initial data satisfying the dominant energy condition

2015/02/26 by Mattias Dahl, Dahl, Mattias, Anna Sakovich +1 · 2 citations
Mathematics · #Advanced Mathematical Physics Problems #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #General Relativity and Quantum Cosmology (gr-qc) #Geometric Analysis and Curvature Flows #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1502.07487

openalex publication_date 2015/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

When working with asymptotically hyperbolic initial data sets for general relativity it is convenient to assume certain simplifying properties. We prove that the subset of initial data sets with such properties is dense in the set of physically reasonable asymptotically hyperbolic initial data sets. More specifically, we show that an asymptotically hyperbolic initial data set with non-negative local energy density can be approximated by an initial data set with strictly positive local energy density and a simple structure at infinity, while changing the mass arbitrarily little. This is achieved by suitably modifying the argument used by Eichmair, Huang, Lee and Schoen in the asymptotically Euclidean case.

Citations

• The mass of an asymptotically flat manifold
• Mass-like invariants for asymptotically hyperbolic metrics

Cited by

• The hyperbolic positive energy theorem
• Existence and uniqueness of constant mean curvature foliations of general asymptotically hyperbolic 3-manifolds

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