Complexity of four dimensional Anti-de-Sitter black holes with a rotating string in generalized scalar-tensor theories.

The present work aims to compute the computational complexity of hairy Anti-de-Sitter black holes in four dimensions according to the Complexity equals Action (CA) conjecture on a generalized scalar-tensor theory. To perform this, the system contains a particle moving on the boundary of AdS$_{4}$, corresponding to the insertion of a fundamental string in the bulk. The effect string is given by the Nambu-Goto term, analyzing the time development of this system, which is affected by the parameters of this class of theory.