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Paper IPM / P / 17171  


Abstract:  
In this paper, we investigate generalized volumecomplexity $\mathcal{C}_{\rm gen}$ for a twosided uncharged HV black brane in $d+2$ dimensions. This quantity which was recently introduced in [arXiv:2111.02429 [hepth]], is an extension of volume in the Complexity=Volume (CV) proposal, by adding higher curvature corrections with a coupling constant $\lambda$ to the volume functional. We numerically calculate the growth rate of $\mathcal{C}_{\rm gen}$ for different values of the hyperscaling violating exponent $\theta$ and dynamical exponent $z$. It is observed that $\mathcal{C}_{\rm gen}$ always grows linearly at late times provided that we choose $\lambda$ properly. Moreover, it reaches to its late time value from below.
%Furthermore, it is an increasing function of $d$, $\theta$ and $\lambda$.
For the case $\lambda=0$, we find an analytic expression for the late time growth rate for arbitrary values of $\theta$ and $z$.
%In this case, $\mathcal{C}_{\rm gen}$ is a decreasing function of $z$.
However, for $\lambda \neq 0$, the late time growth rate can only be calculated analytically for some specific values of $\theta$ and $z$. We also examine the dependence of the growth rate on $d$, $\theta$, $z$ and $\lambda$. Furthermore, we calculate the complexity of formation obtained from volumecomplexity.
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