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General Relativity and Quantum Cosmology

arXiv:0710.3365 (gr-qc)
[Submitted on 17 Oct 2007 (v1), last revised 9 Mar 2008 (this version, v2)]

Title:Singular Yamabe metrics and initial data with exactly Kottler-Schwarzschild-de Sitter ends

Authors:Piotr T. Chrusciel, Daniel Pollack
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Abstract: We construct large families of initial data sets for the vacuum Einstein equations with positive cosmological constant which contain exactly Delaunay ends; these are non-trivial initial data sets which coincide with those for the Kottler-Schwarzschild-de Sitter metrics in regions of infinite extent. From the purely Riemannian geometric point of view, this produces complete, constant positive scalar curvature metrics with exact Delaunay ends which are not globally Delaunay. The ends can be used to construct new compact initial data sets via gluing constructions. The construction provided applies to more general situations where the asymptotic geometry may have non-spherical cross-sections consisting of Einstein metrics with positive scalar curvature.
Comments: Minor changes, updated references. Final version. To appear in Annales Henri Poincare
Subjects: General Relativity and Quantum Cosmology (gr-qc); Differential Geometry (math.DG)
Cite as: arXiv:0710.3365 [gr-qc]
  (or arXiv:0710.3365v2 [gr-qc] for this version)
  https://doi.org/10.48550/arXiv.0710.3365
Journal reference: AnnalesHenriPoincare9:639-654,2008
Related DOI: https://doi.org/10.1007/s00023-008-0368-6

Submission history

From: Daniel Pollack [view email]
[v1] Wed, 17 Oct 2007 18:07:29 UTC (28 KB)
[v2] Sun, 9 Mar 2008 02:07:43 UTC (29 KB)
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