For Lovelock black holes, the Complexity=Action growth rate at late times is a coupling-independent multiple of the mass, and the Schwarzschild limit is recovered only up to a constant under the authors' boundary-term prescription.
Action growth rate for a higher curvature gravitational theory
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abstract
In this paper, we use the "complexity equals action" (CA) conjecture to discuss the action growth rate in a black hole with multiple Killing horizons for a higher curvature theory of gravity. Based on the Noether charge formalism of Iyer and Wald, a general formalism can be resorting to finding the action growth rate within the WDW patch at the late time approximation. Moreover, as an application, we apply this formalism to a $U(1)$ invariance matter fields and utilise our results in two specific cases. Our results are universal and can be considered as the extension of the asymptotic AdS to the arbitrary asymptotic one.
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Time dependence of complexity for Lovelock black holes
For Lovelock black holes, the Complexity=Action growth rate at late times is a coupling-independent multiple of the mass, and the Schwarzschild limit is recovered only up to a constant under the authors' boundary-term prescription.