# Complexity growth rates for AdS black holes in massive gravity and $f(R)$ gravity

## TL;DR

This paper investigates the growth rates of quantum complexity in various AdS black holes within massive gravity and $f(R)$ gravity, analyzing how different parameters influence the complexity evolution.

## Contribution

It provides the first detailed computation of action growth rates for black holes in massive gravity and $f(R)$ gravity, exploring effects of graviton mass, higher derivatives, and topology.

## Key findings

- Massive gravity and $f(R)$ gravity alter complexity growth rates.
- Black hole charge and topology significantly influence the action growth.
- Higher derivative terms impact the late-time complexity evolution.

## Abstract

The "complexity = action" duality states that the quantum complexity is equal to the action of the stationary AdS black holes within the Wheeler-DeWitt patch at late time approximation. We compute the action growth rates of the neutral and charged black holes in massive gravity and the neutral, charged and Kerr-Newman black holes in $f(R)$ gravity to test this conjecture. Besides, we investigate the effects of the massive graviton terms, higher derivative terms and the topology of the black hole horizon on the complexity growth rate.