The globally hyperbolic metric splitting for non-smooth wave-type space-times
Mathematical Physics
2014-06-30 v2 General Relativity and Quantum Cosmology
Classical Analysis and ODEs
Differential Geometry
math.MP
Abstract
We investigate a generalization of the so-called metric splitting of globally hyperbolic space-times to non-smooth Lorentzian manifolds and show the existence of this metric splitting for a class of wave-type space-times. Our approach is based on smooth approximations of non-smooth space-times by families (or sequences) of globally hyperbolic space-times. In the same setting we indicate as an application the extension of a previous result on the Cauchy problem for the wave equation.
Keywords
Cite
@article{arxiv.1310.1310,
title = {The globally hyperbolic metric splitting for non-smooth wave-type space-times},
author = {Günther Hörmann and Clemens Sämann},
journal= {arXiv preprint arXiv:1310.1310},
year = {2014}
}
Comments
18 pages, 1 figure, v2: minor changes suggested by the referees, J. Math. Anal. Appl. (2014)