Holographic complexity and action growth in massive gravities

TL;DR

This paper studies how the growth rate of holographic complexity, measured by action in the Wheeler-DeWitt patch, behaves in massive gravity models, revealing universal behaviors and differences between neutral and charged black holes.

Contribution

It demonstrates the universal late-time behavior of action growth in massive gravity and compares the computational speeds of neutral and charged black holes with Einstein gravity.

Findings

Neutral black holes have the same action growth rate as Einstein gravity when mass is fixed.

Charged black holes in massive gravity have higher action growth rates than in Einstein gravity.

Massive charged black holes are faster computationally than their Einstein gravity counterparts.

Abstract

In this paper, we investigate the growth rates of action for the anti-de Sitter black holes in massive-Einstein gravity models and obtain the universal behaviors of the growth rates of action (the rates of holographic complexity) within the "Wheeler-DeWitt"(WDW) patch at the late limit. Furthermore, we find that, for the static neutral cases, when the same mass of black holes is given, the computational speed of the neutral massive black hole is the same as its Einstein gravity counterpart, which is independent with the effect of the graviton mass terms, nevertheless, for the static charged cases, when the same mass and charge parameters of black holes are given, the growth rates of action for the massive charged black holes are always superior to the growth rates of action without graviton mass terms, which directly shows that the massive charged black holes as computers on the computational speeds are faster than their Einstein gravity counterparts.