On Complexity Growth in Minimal Massive 3D Gravity

TL;DR

This work computes the rate of holographic complexity growth using the complexity = action (CA) prescription for BTZ black holes within Minimal Massive 3D Gravity (MMG), a model designed to resolve bulk-boundary clashes in TMG. By evaluating the on-shell action on Wheeler-DeWitt patches and incorporating the well-defined Gibbons-Hawking boundary term, the authors derive a closed form for the CA growth rate that depends on MMG parameters and horizon data. They show that, for vanishing inner horizon ($r_- \to 0$), the CA growth rate saturates the Lloyd-type bound with the physical mass $\mathcal{M}_{MMG}$, and confirm the TMG limit ($\alpha \to 0$) yields the corresponding saturation with $\mathcal{M}_{TMG}$. These results support the picture of black holes as the fastest information-processing systems in these gravity theories and motivate further investigations in related higher-derivative models.

Abstract

We study the complexity growth by using complexity = action (CA) proposal in Minimal Massive 3D Gravity(MMG) model which is proposed for resolving the bulk-boundary clash problem of Topologically Massive Gravity(TMG). We observe that the rate of the complexity growth for BTZ black hole saturates the proposed bound by physical mass of the BTZ black hole in the MMG model, when the angular momentum parameter and the inner horizon of black hole goes to zero.