Black Hole Entropy and Complexity Growth in Horndeski Gravity within the AdS/BCFT Framework

Abstract

This work investigates the connection between quantum complexity and gravitational dynamics within the framework of Horndeski gravity, extending the AdS/BCFT correspondence to include scalar-tensor interactions. By refining the "complexity=action" conjecture, we analyze how Horndeski gravity modifies the Wheeler-DeWitt patch and the causal structure relevant for holographic complexity. Our analysis shows that the linear growth of complexity, proportional to the product of black hole entropy and temperature, is recovered for the class of black hole configurations studied here, including rotating and charged solutions. We also study the effect of shock waves on complexity growth and find the appearance of the switchback effect. These conclusions hold in the regime in which the relevant effective characteristic cone of Horndeski gravity is compatible with the null structure used to define the Wheeler-DeWitt patch, so that the causal construction effectively matches that of the background metric. Within this domain of validity, our results provide evidence for the complexity=action conjecture in Horndeski gravity and illustrate how modified gravitational couplings affect holographic complexity in the AdS/BCFT framework.