Islands in Kerr-Newman Black Holes

TL;DR

The paper tackles the Kerr-Newman black hole information paradox by leveraging the island paradigm. Through a near-horizon reduction to an effective $2$D theory and $CFT_2$ entanglement entropy, it derives Page curves for non-extremal black holes, showing a transition from linear entropy growth to saturation once an island appears, with a Page time scaling as $t_{ ext{Page}} obreak= obreak rac{6}{c\kappa}S_{ ext{BH}}$. It further analyzes how angular momentum $a$ and charge $Q$ affect $t_{ ext{Page}}$ and $t_{ ext{scr}}$, noting divergences at extremality. In the near-extremal regime, Kerr/CFT and warped AdS$_3$ geometry lead to Schwarzian-dominated dynamics, yielding one-loop corrections and quantum delays that keep the entropy finite, thereby reinforcing information conservation and extending the island framework to general stationary spacetimes.

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.

Figures (6)

• Figure 1: The Penrose diagram for Kerr-Newman black holes. These dash lines are labeled by event horizons, which divides the whole spacetime into four wedges. $R_{\pm}$ represents the left and right wedge where Hawking radiation exists.
• Figure 2: The Penrose diagram for non-extremal Kerr-Newman black holes by considering the entanglement island. The blue line represents the region of radiation where the Hawking radiation is collected by the asymptotical observer. The red line represents the region of island. The points $a_{\pm} / b_{\pm}$ are denoted by endpoints of island/radiation.
• Figure 3: The time evolution of entanglement entropy of non-extremal eternal Kerr-Newman black holes. The red line represents the entropy without island. While the blue line represents the entropy with a single island. The Page curve is represented by the solid line.
• Figure 4: The Page time as a function for the angular momentum $a$ and the charge $Q$ (in the unit of $\frac{6\pi}{cG_N})$. On the left, the charge $Q$ is fixed; On the right, the angular momentum $a$ is fixed. Note that in the extremal case, the Page time is divergent.
• Figure 5: The scrambling time as a function for the angular momentum $a$ and the charge $Q$. Here we set $G_N=1$. (a) The charge is fixed. (b) The angular momentum is fixed. (c) is the zoomed plot of (b).