The Strong Cosmic Censorship Conjecture

TL;DR

The paper surveys the Strong Cosmic Censorship problem and its modern formulation via the maximal globally hyperbolic development ($\mathrm{MGHD}$), clarifying how inextendibility of the MGHD preserves determinism in general relativity. It lays out the central mechanisms (notably the Cauchy horizon blue-shift instability and mass inflation) that shape interior singularity formation, and it reviews rigorous results across symmetry classes—from Minkowski stability to spherical collapse and two-ended black holes—highlighting when $C^0$, $H^1$, or $C^2$ extendibility is ruled out. It connects exterior decay tails (Price’s law) and late-time behavior to interior dynamics, showing that linear and nonlinear analyses in various models yield a nuanced picture: some scenarios support SCC while others admit extendible interiors under generic perturbations, especially in the presence of a cosmological constant or higher dimensions. The article also outlines the open problems and future directions needed to achieve a full, non-symmetric resolution, including understanding endstates of gravitational collapse, multiple-black-hole interactions, and the role of realistic matter models beyond vacuum and scalar fields.

Abstract

In the wake of major breakthroughs in General Relativity during the 1960s, Roger Penrose introduced Strong Cosmic Censorship, a profound conjecture regarding the deterministic nature of the theory. Penrose's proposal has since opened far-reaching new mathematical avenues, revealing connections to fundamental questions about black holes and the nature of gravitational singularities. We review recent advances arising from modern techniques in the theory of partial differential equations as applied to Strong Cosmic Censorship, maintaining a focus on the context of gravitational collapse that gave birth to the conjecture.

Figures (9)

• Figure 1: Future analytic extension of the Kerr metric. $\mathcal{CH}^+$ is a (smoothly extendible) Cauchy horizon emanating from timelike infinity $i^+$, and $\mathcal{T}$ a timelike ring singularity.
• Figure 2: Schwarzschild as the MGHD of a two-ended asymptotically flat hypersurface $\Sigma$.
• Figure 3: Penrose diagram of Oppenheimer--Snyder OppenheimerSnyder spacetime (gravitational collapse).
• Figure 4: Left: Penrose diagram of a naked singularity spacetime. Right: Penrose diagram of a spacetime with a locally naked singularity inside a black hole.
• Figure 5: Blue-shift effect at the Reissner--Nordström/Kerr Cauchy horizon, figure from blueyakovM.

Theorems & Definitions (37)

• Conjecture 1.1: Strong Cosmic Censorship, modern formulation
• Remark
• Definition 2.1: Cauchy surface
• Definition 2.2: Globally hyperbolic spacetime
• Definition 2.3
• Theorem 2.4: GHDdezorn
• Remark
• Remark
• Theorem 2.5: Penrosesing
• Theorem 3.1: C0mink