In Gauss-Bonnet AdS5, the probe-string complexity growth is maximized at zero velocity, independent of the GB coupling when stationary, and linear in temperature.
Complexity growth rates for AdS black holes in massive gravity and $f(R)$ gravity
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abstract
The "complexity = action" duality states that the quantum complexity is equal to the action of the stationary AdS black holes within the Wheeler-DeWitt patch at late time approximation. We compute the action growth rates of the neutral and charged black holes in massive gravity and the neutral, charged and Kerr-Newman black holes in $f(R)$ gravity to test this conjecture. Besides, we investigate the effects of the massive graviton terms, higher derivative terms and the topology of the black hole horizon on the complexity growth rate.
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$R^2$ corrections to Complexity Growth with a Probe String
In Gauss-Bonnet AdS5, the probe-string complexity growth is maximized at zero velocity, independent of the GB coupling when stationary, and linear in temperature.