Holographic complexity for nonlinearly charged Lifshitz black holes

TL;DR

This paper investigates the late-time growth of holographic complexity in nonlinear charged Lifshitz black holes using the 'complexity=action' approach, revealing conditions under which the Lloyd bound is satisfied or violated.

Contribution

It introduces a study of holographic complexity for nonlinear charged Lifshitz black holes, analyzing the impact of horizon structure and coupling constants on complexity growth bounds.

Findings

For two-horizon black holes, the action growth bound holds.

Single-horizon black holes may violate the Lloyd bound depending on parameters.

The study extends understanding of complexity in non-AdS holographic models.

Abstract

Using "complexity=action" proposal we study the late time growth rate of holographic complexity for nonlinear charged Lifshitz black hole with a single horizon or two horizons. As a toy model, we consider two kinds of such black holes: nonlinear charged Lifshitz black hole and nonlinear logarithmic charged Lifshitz black hole. We find that for the black hole with two horizons, the action growth bound is satisfied. But for the black hole with a single horizon, whether the Lloyd bound is violated depends on the specific value of dimensionless coupling constants $\beta_{1},\beta_{2}$, spacetime dimension $D$ and dynamical exponent $z$.