Gluing Initial Data Sets for General Relativity

Details Gluing Initial Data Sets for General Relativity Gluing Initial Data Sets for General Relativity

2004-09-10

arxiv.org/abs/gr-qc/0409047v1

Phys.Rev.Lett. 93 (2004) 081101

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

Final published version - PRL, 4 pages

Scientific paper

10.1103/PhysRevLett.93.081101

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. Secondly, 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.

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