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. We first consider the quantum field in the four-dimensional Kerr-Newman spacetime. By employing the near-horizon limit, we demonstrate that the field can be effectively described by a reduced two-dimensional field theory. Consequently, the formula of entanglement entropy in CFT$_2$ can be naturally adapted to this reduced two-dimensional theory. Under the framework of this reduced two-dimensional theory, we show that the entanglement entropy of radiation for the non-extremal case satisfies the unitarity in the later stage of the appearance of the entanglement islands. We further examine the impact of angular momentum and charges on the Page time and the scrambling time. Both quantities increases as the angular momentum increases, while decreases as the charge increases. At last, we consider 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. Our findings further substantiate the conservation of information and extend the applicability of the island paradigm to the most general stationary spacetime background.