For an eternal black hole, the interior partition function factorizes as the square of the exterior one, fixing the behind-the-horizon cutoff in terms of the UV cutoff.
More on Complexity in Finite Cut Off Geometry
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abstract
It has been recently proposed that late time behavior of holographic complexity in a uncharged black brane solution of Einstein-Hilbert theory with boundary cut off is consistent with Lloyd's bound if we have a cut off behind the horizon. Interestingly, the value of this new cut off is fixed by the boundary cut off. In this paper, we extend this analysis to the charged black holes. Concretely, we find the value of this new cut off for charged small black hole solutions of Einstein-Hilbert-Maxwell theory, in which the proposed bound on the complexification is saturated. We also explore this new cut off in Gauss-Bonnet-Maxwell theory.
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An Infalling Observer and Behind the Horizon Cutoff
For an eternal black hole, the interior partition function factorizes as the square of the exterior one, fixing the behind-the-horizon cutoff in terms of the UV cutoff.