# On Complexity for Higher Derivative Gravities

## TL;DR

This paper investigates the complexity growth in higher derivative gravity theories, including critical gravity, showing saturation of the proposed bound for neutral black holes and analyzing how shock waves and massive modes influence growth rates.

## Contribution

It introduces the study of complexity growth in higher derivative gravities using the 'complexity=action' proposal, highlighting effects of massive modes and shock waves.

## Key findings

- Complexity growth saturates the bound for neutral black holes.
- Massive spin-2 modes slow down complexity growth.
- Shock waves influence the rate of complexity increase.

## Abstract

Using "complexity=action" proposal we study complexity growth of certain gravitational theories containing higher derivative terms. These include critical gravity in diverse dimensions. One observes that the complexity growth for neutral black holes saturates the proposed bound when the results are written in terms of physical quantities of the model. We will also study effects of shock wave to the complexity growth where we find that the presence of massive spin-2 mode slows down the rate of growth.