Generalised hyperbolicity in spacetimes with Lipschitz regularity
General Relativity and Quantum Cosmology
2017-02-14 v3 Analysis of PDEs
Abstract
In this paper, we obtain general conditions under which the wave equation is well-posed in spacetimes with metrics of Lipschitz regularity. In particular, the results can be applied to spacetimes where there is a loss of regularity on a hypersurface such as shell-crossing singularities, thin shells of matter and surface layers. This provides a framework for regarding gravitational singularities, not as obstructions to the world lines of point-particles, but rather as an obstruction to the dynamics of test fields.
Cite
@article{arxiv.1507.06463,
title = {Generalised hyperbolicity in spacetimes with Lipschitz regularity},
author = {Yafet Sanchez Sanchez and James A. Vickers},
journal= {arXiv preprint arXiv:1507.06463},
year = {2017}
}