Action growth rate for a higher curvature gravitational theory

Understand

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.