Islands in Kerr–Newman black holes

Abstract We investigate the information paradox in the four-dimensional Kerr–Newman black hole by employing the recently proposed island paradigm. To accurately capture the behavior of entanglement entropy in Kerr–Newman spacetime, we analyze the form of quantum fields in the near-horizon limit. We demonstrate the field can be effectively described by a reduced two-dimensional field theory. Under the framework of this reduced two-dimensional theory, the entanglement entropy of radiation satisfies the Page curve. We also examine the impact of angular momentum and charges on the Page time and the scrambling time. A step further, we concentrate on analyzing the near extremal case. Resort to the Kerr/CFT correspondence, the near-horizon geometry of near extremal Kerr–Newman black holes can be taken account for a warped AdS geometry. In this scenario, the low-energy effective degrees of freedom are dominated by the Schwarzian zero mode, resulting in a one-loop correction to the partition function. The entanglement entropy is subsequently recalculated under the thermodynamic with corrections. Through explicit calculations, we finally find that the Page time and the scrambling time exhibits quantum delays. This strongly suggests that the near extremal geometry is governed by the Schwarzian dynamics, in which quantum fluctuations result in a reduced rate of information leakage. Moreover, we provide a rigorous discussion on the validity of the island formula and compute the entanglement entropy in Kerr–Newman AdS spacetime as a supplementary example. Our findings further substantiate information conservation and extend the island paradigm to the most general class of stationary spacetime.