A new look at the C 0-formulation of the strong cosmic censorship conjecture

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.

Keywords

• strong cosmic censorship
• black holes
• quantum computational complexity