A New Look at the $C^{0}$-formulation of the Strong Cosmic Censorship Conjecture

TL;DR

This paper investigates the $C^{0}$-formulation of the strong cosmic censorship conjecture through a quantum complexity lens, revealing potential violations and implications for black hole geometry and holography.

Contribution

It introduces a quantum complexity-theoretic approach to analyze the $C^{0}$-formulation of the SCC and demonstrates its violation in certain hyperbolic AdS black hole scenarios.

Findings

The $C^{0}$-SCC may not hold for generic black hole initial conditions.

Violations of the $C^{0}$-SCC correspond to violations of the complexity=volume conjecture.

The analysis links black hole interior extendability to quantum complexity bounds.

Abstract

We examine the $C^{0}$-formulation of the strong cosmic censorship conjecture (SCC) from a quantum complexity-theoretic perspective and argue that for generic black hole parameters as initial conditions for the Einstein equations, corresponding to the expected geometry of a hyperbolic black hole, the metric is $C^{0}$-extendable to a larger Lorentzian manifold across the Cauchy horizon. To demonstrate the pathologies associated with a hypothetical validity of the $C^{0}$ SCC, we prove it violates the "complexity=volume" conjecture for a low-temperature hyperbolic AdS$_{d+1}$ black hole dual to a CFT living on a ($d-1$)-dimensional hyperboloid $H_{d-1}$, where in order to preserve the gauge/gravity duality we impose a lower bound on the interior metric extendability of order the classical recurrence time.