# Complexity and Near Extremal Charged Black Branes

## TL;DR

This paper calculates the holographic complexity of near extremal charged black branes in various dimensions using two methods, revealing their equivalence under certain cutoff and counterterm conditions, and extends the analysis to Vaidya charged black branes.

## Contribution

It introduces two approaches to compute holographic complexity for near extremal charged black branes and demonstrates their equivalence under specific cutoff and counterterm assumptions.

## Key findings

- Complexity calculations from both methods agree under cutoff and counterterm conditions.
- The approach is extended to Vaidya charged black branes.
- Results provide insights into holographic complexity near extremality.

## Abstract

We compute holographic complexity of charged black brane solutions in arbitrary dimensions for the near horizon limit of near extremal case using two different methods. The corresponding complexity may be obtained either by taking the limit from the complexity of the charged black brane, or by computing the complexity for near horizon limit of near extremal solution. One observes that these results coincide if one assumes to have a cutoff behind horizon whose value is fixed by UV cutoff and also taking into account a proper counterterm evaluated on this cutoff. We also consider the situation for Vaidya charged black branes too.