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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 investigate how Horndeski gravity modifies the Wheeler-DeWitt patch and the causal structure of the black hole. Our analysis reveals that the linear growth of complexity, proportional to the product of black hole entropy and temperature, remains valid across various black hole configurations, including those of rotating and charged black holes. Moreover we study the impact of shock waves on the growth of complexity, which shows the appearance of the ``switchback effect''. These results show the universality of the complexity = action conjecture and its validity in modified gravitational theories.