SciPost Phys. 7, 073 (2019) ·
published 3 December 2019
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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.
