Action growth rate for a higher curvature gravitational theory

TL;DR

This paper investigates the rate of action growth in black holes within higher curvature gravity theories using the complexity equals action conjecture, extending previous results to more general asymptotic conditions.

Contribution

It develops a universal formalism based on Noether charge for calculating action growth in higher curvature gravity, applicable to black holes with multiple horizons and arbitrary asymptotics.

Findings

Derived a general expression for action growth rate in higher curvature theories.

Applied the formalism to U(1) matter fields in specific black hole solutions.

Extended the complexity-action relation to broader asymptotic spacetime geometries.

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.