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Using Papadodimas and Raju construction of operators describing the interiorof a black hole, we present a general relation between partition functions ofoperators describing inside and outside the black hole horizon. In particularfor an eternal black hole the partition function of the interior modes may begiven in terms those partition functions associated with the modes of left andright exteriors. By making use of this relation we observe that setting afinite UV cutoff will enforce us to have a cutoff behind the horizon whosevalue is fixed by the UV cutoff. The resultant cutoff is in agreement with whatobtained in the context of holographic complexity.

An Infalling Observer and Behind the Horizon Cutoff