On the space of initial values strictly satisfying the dominant energy condition

Abstract

The dominant energy condition imposes a restriction on initial value pairs found on a spacelike hypersurface of a Lorentzian manifold. In this article, we study the space of initial values that satisfy this condition strictly. To this aim, we introduce an index difference for initial value pairs and compare it to its classical counterpart for Riemannian metrics. Recent non-triviality results for the latter will then imply that this space has non-trivial homotopy groups.

arXiv commentFinal version. Published in Mathematische Annalen

References in corpus (7)

• Generalized Cylinders in Semi-Riemannian and Spin Geometry
• Infinite loop spaces and positive scalar curvature
• The space of metrics of positive scalar curvature
• Harmonic spinors and metrics of positive curvature via the Gromoll filtration and Toda brackets
• Conjectures on Convergence and Scalar Curvature
• Positive scalar curvature on ${\mathbf{Pin}}^{\pm }$- and ${\mathbf{Spin}}^c$-manifolds
• An Enlargeability Obstruction for Spacetimes with both Big Bang and Big Crunch

Cited by in corpus (1)

• Initial data sets with dominant energy condition admitting no smooth dec spacetime extension