Strong Cosmic Censorship (SCC) Conjecture

Prove the strong cosmic censorship conjecture by establishing that, for generic asymptotically flat initial data for Einstein’s equations, the maximal Cauchy development is inextendible, thereby ruling out extendible spacetimes with Cauchy horizons under generic perturbations.

Background

The paper analyzes Hawking-mode effective temperatures perceived by freely falling observers in Reissner–Nordström–(anti-)de Sitter spacetimes, with particular attention to the inner (Cauchy) horizon and implications for strong cosmic censorship (SCC). The inner horizon is known to exhibit infinite blueshift and associated mass inflation under perturbations, motivating SCC.

Historically, the presence of a positive cosmological constant can introduce redshift effects that may counter blueshift near the inner horizon, raising questions about whether the Cauchy horizon might persist without forming a singularity. The paper evaluates this interplay using the effective-temperature formalism and compares with results based on the quantum stress–energy tensor.

Within this context, the authors restate the precise formulation of SCC as an inextendibility statement for the maximal Cauchy development under generic asymptotically flat initial data, framing the broader conjectural backdrop against which their calculations are assessed.

References

The strong cosmic censorship conjecture, in its precise definition [PenroseGR_1980,Christodoulou_2008], states that for generic asymptotically flat initial conditions for Einstein's equations, the maximal Cauchy development is inextendible.

— Hawking radiation inside a charged, cosmological black hole  (2408.13955 - Ravuri et al., 2024) in Subsection “Divergence at the inner horizon and on the validity of the SCC conjecture”

What replaces the Cauchy horizon, and in which geometry the interior terminates, is one of the sharpest open questions of classical gravity.

— Emergent Scaling Symmetry and Universal Interior Criticality of Scalarized Black Holes  (2609.30240 - Sun et al., 24 Sep 2026) in Introduction

The regularity of the inner Cauchy horizon remains open for these spacetimes.

— Naked Singularities beyond Spherical Symmetry: Instability of $κ$-Self-Similar Solutions via an Iteration Scheme  (2609.04723 - An et al., 4 Sep 2026) in Section 1, subsection “Background”

The modern formulation of the strong cosmic censorship conjecture, due to Christodoulou , states that the maximal globally hyperbolic development of generic asymptotically flat or compact initial data for the (vacuum) Einstein equations is inextendible as a Lorentzian manifold with a continuous metric and locally square-integrable Christoffel symbols.

— Spherically symmetric inextendibility of weak null singularities with Christoffel symbols in $L^s_{\text{loc}}$  (2609.05167 - Cameron et al., 4 Sep 2026) in Section 1, Introduction

The third question is nonlinear and global: if a background inner horizon exists and the scalaron is locally non-tachyonic, does the Cauchy horizon survive generic perturbations?

— Beyond the Dolgov-Kawasaki instability: Covariant scalaron stability, entropy transport, and inner horizons in f(R) gravity  (2610.11649 - Lobo et al., 8 Oct 2026) in Section 5.3, “Layer III: Cauchy-horizon stability”