\documentclass[12pt]{article}
\usepackage{amsmath,amssymb,amsfonts}
\begin{document}
We employ the âcomplexity equals action" conjecture to investigate the action growth rate for charged and neutral AdS black branes of a holographic toy model consisting of Einstein-Maxwell theory in d + 1-dimensional bulk spacetime with d-1 massless scalar fields which is called Einstein-Maxwell-Axion (EMA) theory. From the holographic point of view, the scalar fields source a spatially dependent field theory with momentum relaxation on the boundary, which is dual to the homogeneous and isotropic black branes. We find that the growth rate of holographic complexity within the Wheeler-DeWitt (WDW) patch is finite for
these solutions at the late time limit. In fact, the momentum relaxation term does not affect the previous results explicitly but changes the value of the mass and provides strong motivations to investigate the vanishing of complexity growth rate at some finite temperature other than zero. Also, we study non-linear contribution of axion field kinetic term in the context of k-essence model in four-dimensional spacetime. We find that in the study of full time dependence, by increasing the coupling of non-linear term, the action growth rate decreases while at late time limit, this modification does not change the growth rate apart from the mass definition.
\end{document}