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

Abstract

The quantum gravitational effects on the region near the horizon may alter the black hole's horizon drastically. The horizon becomes partially reflective, portrayed by a quantum membrane. With this modification, the object can be considered as an exotic compact object (ECO). Therefore, the existence of a quantum membrane makes the properties of the black holes differ from those of ECOs. Furthermore, quantum effects on the strong gravitational regime may also give rise to a nonconserved matter tensor that can be described phenomenologically using Rastall theory of gravity.In this work, we study the properties of the black holes and ECOs within Rastall theory of 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 black holes, and reveal its hidden conformal symmetry. The Cardy microscopic entropy formula and absorption crosssections from 2D CFT are computed and then matched with gravity calculation. We also extend the dual CFT analysis for studying the properties of ECOs that resemble Kerr-Newman-NUT-Kiselev black holes in Rastall gravity to see the role of the reflective quantum membrane. The existence of the quantum membrane leads to the appearance of the gravitational echoes in ringdown signal from the gravitational wave observations 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 for ECOs. 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 in the absorption cross-section of both objects. We obtain that the echo time delay of the ringdown signal depends explicitly on the Rastall coupling constant. This coupling constant may play the 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. Therefore, the echo time-delay observation could be used to constrain the coupling constant of Rastall gravity.