On Lorentzian causality with continuous metrics

Details On Lorentzian causality with continuous metrics On Lorentzian causality with continuous metrics

2011-11-02

arxiv.org/abs/1111.0400v2

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

36 pages, 15 figures. Minor corrections, a proof made more explicit. One of the main results strengthened to show that Lipschi

Scientific paper

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 $C^{0,1}$ differentiability of the metric suffices for many key results of the smooth causality theory.

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