Complexity growth of massive black hole with a probe string

TL;DR

This paper investigates how the complexity of a massive gravity black hole system evolves over time, focusing on the effects of a probe string modeled by the Nambu-Goto action, and explores how graviton mass and horizon curvature influence this complexity.

Contribution

It introduces a detailed analysis of the complexity growth in massive gravity via the 'Complexity = Action' conjecture, incorporating a probe string and examining the effects of graviton mass and curvature.

Findings

Complexity growth is affected by graviton mass.

Horizon curvature influences the Nambu-Goto contribution.

The study reveals new properties of complexity in massive gravity.

Abstract

In this work, we study the computational complexity of massive gravity theory via the "Complexity = Action" conjecture. Our system contains a particle moving on the boundary of the black hole spacetime. It is dual to inserting a fundamental string in the bulk background. Then this string would contribute a Nambu-Goto term, such that the total action is composed of the Einstein-Hilbert term, Nambu-Goto term and the boundary term. We shall investigate the time development of this system, and mainly discuss the features of the Nambu-Goto term affected by the graviton mass and the horizon curvature in different dimensions. Our study could contribute interesting properties of complexity.