Gluing Initial Data Sets for General Relativity

2004/08/18 by Piotr T. Chruściel, Piotr T. Chrusciel, James Isenberg +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Geometry Research #Black Holes and Theoretical Physics #Cosmology and Gravitation Theories #gr-qc #math.DG

paper · pdf · doi:10.1103/physrevlett.93.081101

published as Phys.Rev.Lett. 93 (2004) 081101 · Final published version - PRL, 4 pages

openalex publication_date 2004/08/18 · arxiv created 2004/09/10 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish an optimal gluing construction for general relativistic initial data sets. The construction is optimal in two distinct ways. First, it applies to generic initial data sets and the required (generically satisfied) hypotheses are geometrically and physically natural. Second, the construction is completely local in the sense that the initial data is left unaltered on the complement of arbitrarily small neighborhoods of the points about which the gluing takes place. Using this construction we establish the existence of cosmological, maximal globally hyperbolic, vacuum space-times with no constant mean curvature spacelike Cauchy surfaces.

Citations

• On the proof of the positive mass conjecture in general relativity

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• Midisuperspacetime foam and the cosmological constant

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