Complexity growth of BTZ black hole in massive gravity with a null string

TL;DR

This paper studies how the complexity growth of a tensionless string near a BTZ black hole horizon in massive gravity differs from tensile strings, proposing a link to RG flow for complexity reconstruction.

Contribution

It introduces the tensionless string limit in massive gravity and explores its impact on complexity growth, highlighting the tension's role and proposing a new RG-based reconstruction method.

Findings

Tensionless strings exhibit distinct complexity growth behavior from tensile strings.

String tension partially influences the complexity growth rate.

A potential RG flow-based approach to reconstruct complexity is proposed.

Abstract

In this paper, we investigate the complexity growth of the tensionless limit of string in the neutral BTZ black hole horizon in massive gravity. When the string approaches the horizon, we observe a novel phenomenon for the Nambu-Goto action growth that produces significant difference from tensile string geometry. The string's tension is then suggested to partially contribute to the growth of the action. We also argue a potential proposal that reconstructs the complexity from the renormalization group (RG) flow.