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

Abstract

There are two versions of the dominant energy condition (=dec): The original one for Lorentzian manifolds and an associated one for initial data sets. If a Lorentzian manifold satisfies dec, then so does the induced initial set on any embedded spacelike hypersurface. In this article, we discuss the question of a potential converse of this: Is every dec initial data set the induced one on a spacelike hypersurface within a suitably chosen dec Lorentzian manifold? We provide an example showing that in general the answer is no if we require all structures to be smooth.

arXiv comment10 pages. Comments welcome!

References in corpus (7)

• A generalization of Hawking's black hole topology theorem to higher dimensions
• Equality in the Spacetime Positive Mass Theorem
• On the geometry and topology of initial data sets with horizons
• Localized deformation for initial data sets with the dominant energy condition
• Reduction Arguments for Geometric Inequalities Associated With Asymptotically Hyperboloidal Slices
• A note on the positive mass theorem with boundary
• On the space of initial values strictly satisfying the dominant energy condition