Strong Cosmic Censorship with bounded curvature

In this paper we propose a weaker version of Penrose’s much heeded Strong Cosmic Censorship (SCC) conjecture, asserting inextendability of maximal Cauchy developments by manifolds with Lipschitz continuous Lorentzian metrics and Riemann curvature bounded in L p . Lipschitz continuity is the threshold regularity for causal structures, while curvature bounds rule out infinite tidal accelerations, arguing for physical significance of this weaker SCC conjecture. The main result of this paper, under the assumption that no extensions exist with higher connection regularity W loc 1 , p , proves in the affirmative this SCC conjecture with bounded curvature for p sufficiently large, ( p > 4 to address uniform bounds, p > 2 without uniform bounds).