Complexity growth for AdS black holes in the presence of backreaction*

Abstract We investigate the holographic complexity in backreacted gravity backgrounds according to the complexity-action conjecture. The backreaction considered here originates from the presence of static strings evenly distributed over the system. We exploit a probe string in the bulk and evaluate the Nambu-Goto action and its dependence on backreaction. The results suggest that, for slower strings, the complexity increases with increasing backreaction, in accordance with the findings of holographic entanglement entropy. However, for faster strings, the situation is different. Furthermore, we analyze the relationship between complexity and space dimension as well as string velocity.