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

Abstract: This work explores the holographic complexity and residual entropy of a rotating BTZ black hole within the framework of Horndeski gravity. The investigation is motivated by the need to understand the emission of information from black holes, as encoded by quantum complexity, which persists even at zero temperature. Traditionally, black holes are considered to cease emitting information upon reaching zero temperature, yet our findings suggest a minimum level of information or minimal entropy. This challenges the classical notion of black hole death. Recent studies in the context of Horndeski gravity and the AdS/BCFT correspondence have identified a non-zero minimal entropy at zero temperature. Our work shows that complexity and entropy provide crucial insights into the information emission from black holes, extending beyond their classical death. These findings significantly affect our understanding of black hole thermodynamics and quantum information theory.