Generalised hyperbolicity in singular space-times

Abstract

A new concept analogous to global hyperbolicity is introduced, based on test fields. It is shown that the space-times termed here ``curve integrable'' are globally hyperbolic in this new sense, and a plausibility argument is given suggesting that the result applies to shell crossing singularities. If the assumptions behind this last argument are valid, this provides an alternative route to the assertion that such singularities do not violate cosmic censorship.

This replacement alters the type of solution considered from "weak" to a solution lying in a specified function space. 9 pages, TeX, eps figure included with psfig