On Lorentzian causality with continuous metrics
General Relativity and Quantum Cosmology
2015-06-03 v3 Mathematical Physics
Differential Geometry
math.MP
Abstract
We present a systematic study of causality theory on Lorentzian manifolds with continuous metrics. Examples are given which show that some standard facts in smooth Lorentzian geometry, such as light-cones being hypersurfaces, are wrong when metrics which are merely continuous are considered. We show that existence of time functions remains true on domains of dependence with continuous metrics, and that differentiability of the metric suffices for many key results of the smooth causality theory.
Keywords
Cite
@article{arxiv.1111.0400,
title = {On Lorentzian causality with continuous metrics},
author = {Piotr T. Chruściel and James D. E. Grant},
journal= {arXiv preprint arXiv:1111.0400},
year = {2015}
}
Comments
Minor changes. Version to appear in Classical and Quantum Gravity