On the space of initial values strictly satisfying the dominant energy condition
Differential Geometry
2023-04-06 v2 General Relativity and Quantum Cosmology
K-Theory and Homology
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.
Keywords
Cite
@article{arxiv.1906.00099,
title = {On the space of initial values strictly satisfying the dominant energy condition},
author = {Jonathan Glöckle},
journal= {arXiv preprint arXiv:1906.00099},
year = {2023}
}
Comments
Final version. Published in Mathematische Annalen