Singularity theorems based on trapped submanifolds of arbitrary co-dimension
General Relativity and Quantum Cosmology
2014-11-21 v2
Abstract
Standard singularity theorems are proven in Lorentzian manifolds of arbitrary dimension n if they contain closed trapped submanifolds of arbitrary co-dimension. By using the mean curvature vector to characterize trapped submanifolds, a unification of the several possibilities for the boundary conditions in the traditional theorems and their generalization to arbitrary co-dimension is achieved. The classical convergence conditions must be replaced by a condition on sectional curvatures, or tidal forces, which reduces to the former in the cases of co-dimension 1, 2 or n.
Cite
@article{arxiv.1005.1249,
title = {Singularity theorems based on trapped submanifolds of arbitrary co-dimension},
author = {Gregory J. Galloway and José M. M. Senovilla},
journal= {arXiv preprint arXiv:1005.1249},
year = {2014}
}
Comments
11 pages, no figures, some corrections.