Rotating black hole with a probe string in Horndeski Gravity

In this work, we present the effect of a probe string on Horndeski's gravity on the complexity of the black hole according to the CA conjecture (Complexity equals action). In our system we consider a rotating black hole in ($2+1$)-spacetime. We consider the effect of the string moving in this spacetime geometry of the black hole BTZ. Thus, for the double description, we have the insertion of a fundamental string in the bulk of spacetime. The effect of this string is given by the Nambu-Goto term. Analyzing the term Nambu-Goto, we can analyze the time of development of this system according to the parameters of Horndeski's gravity. In ours we show some interesting properties of complexity for this severity.