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

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Abstract

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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References

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Acknowledgements

We thank James Isenberg and John M. Lee for helpful conversations.

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Authors and Affiliations

  1. Department of Mathematical Sciences, MSC 110, Lewis and Clark College, 0615 S.W. Palatine Hill Road, Portland, OR, 97219, USA

    Paul T. Allen & Iva Stavrov Allen

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  1. Paul T. Allen
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  2. Iva Stavrov Allen
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Correspondence to Paul T. Allen.

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Communicated by James A. Isenberg.

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Allen, P.T., Allen, I.S. Smoothly Compactifiable Shear-Free Hyperboloidal Data is Dense in the Physical Topology. Ann. Henri Poincaré 18, 2789–2814 (2017). https://doi.org/10.1007/s00023-017-0565-2

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  • DOI: https://doi.org/10.1007/s00023-017-0565-2

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