Generalised hyperbolicity in spacetimes with Lipschitz regularity

摘要

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 obstruction to the dynamics of test fields. Published by AIP Publishing.