# More on Complexity in Finite Cut Off Geometry

## TL;DR

This paper investigates the late-time behavior of holographic complexity in charged black holes with boundary cutoffs, extending previous work on uncharged black branes and exploring the implications for Lloyd's bound.

## Contribution

It extends the analysis of boundary and behind-horizon cutoffs to charged black holes and Gauss-Bonnet-Maxwell theory, identifying the cutoff values that saturate the complexity bound.

## Key findings

- Derived the cutoff value for charged small black holes in Einstein-Hilbert-Maxwell theory.
- Extended the cutoff analysis to Gauss-Bonnet-Maxwell theory.
- Confirmed the saturation of Lloyd's bound in these charged black hole solutions.

## 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.