Time Dependence of Holographic Complexity in Gauss-Bonnet Gravity

We study the effect of the Gauss-Bonnet term on the complexity growth rate of dual field theory using the "Complexity--Volume" (CV) and CV2.0 conjectures. We investigate the late time value and full time evolution of the complexity growth rate of the Gauss-Bonnet black holes with horizons with zero curvature ($k=0$), positive curvature ($k=1$) and negative curvature ($k=-1$) respectively. For the $k=0$ and $k=1$ cases we find that the Gauss-Bonnet term suppresses the growth rate as expected, while in the $k=-1$ case the effect of the Gauss-Bonnet term may be opposite to what is expected. The reason for it is briefly discussed, and the comparison of our results to the result obtained by using the "Complexity--Action" (CA) conjecture is also presented. We also briefly investigate two proposals applying some generalized volume functionals dual to the complexity in higher curvature gravity theories, and find their behaviors are different for $k=0$ at late times.