CAUSALITY AND CAUCHY HORIZONS

Let S be a partial Cauchy surface for (M, g0) which remains a partial Cauchy surface under small metric perturbations. In general, the Cauchy horizon H+(g0, S) may be unstable to small changes in the metric. Points of the horizon may move by large amounts and even the topological type of the horizon may change under arbitrarily small changes in the metric tensor. In this paper, we investigate sufficient conditions for existential, locational, and topological stability of Cauchy horizons under metric changes which perturb the light cones by small amounts.