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| Paper IPM / P / 17171 | ||||||||||||||||||
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In this paper, we investigate generalized volume-complexity Cgen for a two-sided uncharged HV black brane in d+2 dimensions. This quantity which was recently introduced in [arXiv:2111.02429 [hep-th]], is an extension of volume in the Complexity=Volume (CV) proposal, by adding higher curvature corrections with a coupling constant λ to the volume functional. We numerically calculate the growth rate of Cgen for different values of the hyperscaling violating exponent θ and dynamical exponent z. It is observed that Cgen always grows linearly at late times provided that we choose λ properly. Moreover, it reaches to its late time value from below.
%Furthermore, it is an increasing function of d, θ and λ.
For the case λ=0, we find an analytic expression for the late time growth rate for arbitrary values of θ and z.
%In this case, Cgen is a decreasing function of z.
However, for λ≠0, the late time growth rate can only be calculated analytically for some specific values of θ and z. We also examine the dependence of the growth rate on d, θ, z and λ. Furthermore, we calculate the complexity of formation obtained from volume-complexity.
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