Holographic complexity and residual entropy of a rotating charged BTZ black hole within Horndeski gravity

This work investigates the holographic complexity and residual entropy of a rotating charged BTZ black hole within Horndeski gravity. The motivation for considering these two fields of investigation is related to the emission of information from the black hole encoded by quantum complexity; even at zero temperature, information is still emitted. In this case, the death of the black hole only occurs classically. In this sense, the entropy of the black hole at zero temperature must still be a minimum of information that is not entirely zero. In recent investigations regarding Horndeski gravity in the AdS/BCFT correspondence, we showed a minimum entropy (residual/remaining entropy) for zero temperature. In this sense, complexity and entropy, as we will show throughout this work, provide information about the emission from a black hole even after its classical death.