  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.
