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Rotating black holes and exotic compact objects in the Kerr/CFT correspondence within Rastall gravity

Quantum gravitational effects on the near horizon may alter the black hole's horizon drastically to be partially reflective, portrayed by a quantum membrane. With this modification, the object can be considered as an exotic compact object (ECO). Quantum effects on the strong gravitational regime may also lead to a non-conserved matter tensor that can be described phenomenologically using Rastall gravity. In this work, we study the properties of black holes and ECOs within Rastall gravity using Kerr/CFT correspondence. We systematically investigate the properties of the most general rotating black hole solutions in Rastall gravity, i.e., Kerr-Newman-NUT-Kiselev, and reveal its hidden conformal symmetry. The Cardy microscopic entropy formula and absorption cross-sections from 2D CFT are computed and then matched with gravity calculation. We also extend the dual CFT analysis for studying the properties of ECOs. The existence of the quantum membrane leads to the appearance of the gravitational echoes that is manifested as an oscillatory feature on the absorption cross-section. We compute the absorption cross-section and quasi-normal modes in the dual CFT picture. We also compare the absorption cross-section of ECOs to that of black holes. We find that the Rastall coupling constant plays a significant role for both objects. We also obtain that the echo time delay depends explicitly on the Rastall coupling constant. This coupling constant may play a role to recover the correction on time delay that is believed as a non-linear physics effect. Henceforth, the signature of the Rastall gravity can be probed from the time-delay observation.