The local extendibility of causal geodesically incomplete space-times is examined. It is shown that for a space-time including an incomplete inextendible causal geodesic curve γ there exists a particular Ck (resp. Ck-) local extension provided that the curvature and its covariant derivatives are uniformly bounded up to order k+1 (resp. k) in a synchronized frame field along a family of causal geodesics in some neighborhood of a final segment of γ and the strong causality condition is satisfied locally.
ASJC Scopus subject areas
- Statistical and Nonlinear Physics
- Mathematical Physics