Smoothly Compactifiable Shear-Free Hyperboloidal Data is Dense in the Physical Topology

We show that any polyhomogeneous asymptotically hyperbolic constant-mean-curvature solution to the vacuum Einstein constraint equations can be approximated, arbitrarily closely in Hölder norms determined by the physical metric, by shear-free smoothly conformally compact vacuum initial data.

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Bibliographic Details
Published in:	Annales Henri Poincaré Vol. 18; no. 8; pp. 2789 - 2814
Main Authors:	Allen, Paul T., Allen, Iva Stavrov
Format:	Journal Article
Language:	English
Published:	Cham Springer International Publishing 01-08-2017 Springer Nature B.V
Subjects:	Approximation Asymptotic properties Classical and Quantum Gravitation Curvature Dynamical Systems and Ergodic Theory Elementary Particles Mathematical and Computational Physics Mathematical Methods in Physics Norms Physics Physics and Astronomy Quantum Field Theory Quantum Physics Relativity Theory Theoretical Topology
Online Access:	Get full text
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Description
Summary:	We show that any polyhomogeneous asymptotically hyperbolic constant-mean-curvature solution to the vacuum Einstein constraint equations can be approximated, arbitrarily closely in Hölder norms determined by the physical metric, by shear-free smoothly conformally compact vacuum initial data.
ISSN:	1424-0637 1424-0661
DOI:	10.1007/s00023-017-0565-2