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

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.

Minor changes, updated references. Final version. To appear in Annales Henri Poincare

Cited by in corpus (6)

• A review of total energy-momenta in GR with a positive cosmological constant
• The Hamiltonian mass of asymptotically Schwarzschild-de Sitter space-times
• Gluing construction of initial data with Kerr-de Sitter ends
• Hamiltonian dynamics in the space of asymptotically Kerr-de Sitter spacetimes
• Numerical construction of initial data for Einstein's equations with static extension to space-like infinity
• Numerical Brill-Lindquist initial data with a Schwarzschildean end at spatial infinity