Causally symmetric spacetimes

Abstract

Causally symmetric spacetimes are spacetimes with J⁺(S) isometric to J⁻(S) for some set S. We discuss certain properties of these spacetimes, showing for example that if S is a maximal Cauchy surface with matter everywhere on S, then the spacetime has singularities in both J⁺(S) and J⁻(S). We also consider totally vicious spacetimes, a class of causally symmetric spacetimes for which I⁺(p) =I⁻(p) =M for any point p in M. Two different notions of stability in general relativity are discussed, using various types of causally symmetric spacetimes as starting points for perturbations.