  Using Papadodimas and Raju construction of operators describing the interior
of a black hole, we present a general relation between partition functions of
operators describing inside and outside the black hole horizon. In particular
for an eternal black hole the partition function of the interior modes may be
given in terms those partition functions associated with the modes of left and
right exteriors. By making use of this relation we observe that setting a
finite UV cutoff will enforce us to have a cutoff behind the horizon whose
value is fixed by the UV cutoff. The resultant cutoff is in agreement with what
obtained in the context of holographic complexity.
