# An Infalling Observer and Behind the Horizon Cutoff

## TL;DR

This paper explores the relationship between interior and exterior black hole operators using the Papadodimas-Raju construction, revealing how UV cutoffs influence the horizon's cutoff and relate to holographic complexity.

## Contribution

It establishes a general relation between partition functions of interior and exterior black hole modes, linking UV cutoffs to horizon cutoffs and holographic complexity insights.

## Key findings

- Finite UV cutoff induces a fixed cutoff behind the horizon.
- Partition functions of interior modes relate to exterior modes in eternal black holes.
- Cutoff values align with holographic complexity results.

## Abstract

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.