Abstract
Based on reasonable assumptions, we propose a new expression for Lloyd's bound, which confines the complexity growth of charged black holes. We then revisit holographic complexity for charged black branes in the presence of a finite cutoff. Using the proposed Lloyd's bound we find a relation between the UV and the behind the horizon cutoff. This is found to be consistent with the factorization of the partition function at leading order in large N. We argue that the result may be thought of as a holographic realization of strong cosmic censorship.
Highlights
There have been a lot of interesting developments in understanding and resolving puzzles related to the interior of black holes, the mysterious part of the spacetime hiding behind the black hole event horizon
In the context of the anti–de Sitter (AdS)=CFT correspondence, in which these paradoxes can be given a sharp form in terms of information processing of the boundary conformal field theory (CFT) [1,2,3,4], a lot of effort has been devoted towards resolving the aforementioned problems using the entanglement structure of spacetime [5,6]
We have seen that a UV finite cutoff enforces a cutoff behind the outer horizon, with an expression determined by the UV cutoff
Summary
There have been a lot of interesting developments in understanding and resolving puzzles related to the interior of black holes, the mysterious part of the spacetime hiding behind the black hole event horizon. Some of the resolutions are even instrumental in understanding the unique nature of entanglement in generic systems of quantum gravity [7,8] These developments motivated a rigorous search for probes both sensitive to the interior of a black hole and which systematically relate to the evolution of operators in the boundary CFT. One efficient way to compute the complexity of a holographic state was proposed in [11,12]—the “complexity 1⁄4 action” (CA) conjecture In this conjecture, the holographic complexity is given by the on-shell action on the Wheeler-DeWitt (WdW) patch which is the domain of dependence of any Cauchy surface in the bulk which intersects the asymptotic boundary on the time slice, Σ, CðΣÞ
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