Entanglement Islands and Thermodynamics of the Black Hole in Asymptotically Safe Quantum Gravity

TL;DR

The paper investigates whether Hawking evaporation in asymptotically safe quantum gravity is compatible with unitary evolution. It analyzes thermodynamic quantities such as Hawking temperature, heat capacity, entropy, and the mass–horizon radius relation for AS black holes with Yukawa-like corrections. It then computes Hawking radiation entanglement entropy with and without islands, showing that islands yield a Page curve and finite late-time entropy, with $t_{Page}$ and $t_{scr}$ consistent with fast scrambling. Overall, the results indicate a finite radiation entropy and unitary evolution, with a horizon remnant and island prescription providing a consistent resolution to the information paradox in this framework.

Abstract

We study thermodynamic properties and the entanglement island of a black hole in asymptotically safe quantum gravity, analyzing key thermodynamic quantities such as the Hawking temperature, heat capacity, and entropy, as well as the mass-horizon radius relation. Unlike Schwarzschild black holes, the temperature decreases with mass near the evaporation endpoint, signaling a phase transition and possible stable remnant. The entanglement entropy of Hawking radiation is obtained both with and without island contributions. Without islands, the radiation entropy grows linearly indefinitely, leading to the information paradox. By including island contributions and extremizing the generalized entropy functional, we resolve this paradox. At late times, the radiation entropy saturates at the Bekenstein-Hawking entropy, confirming unitary evolution. From this, we derive the Page time and scrambling time by equating early- and late-time entanglement entropies. The result of this study establishes the finiteness of the radiation entropy and consistency with quantum mechanics.

Figures (9)

• Figure 1: The profile of $f(r)$ with respect to $r$ for various of $S_{0}$ by considering $M=1$, $S_{2}=1$, $m_{2}^{2}=2.5 M_{pl}^{2}$ and $m_{0}^{2}=0.095 M_{pl}^{2}$Pawlowski:2023dda.
• Figure 2: The profile of $g(r)$ with respect to $r$ for various of $S_{0}$ by considering $M=1$, $S_{2}=1$, $m_{2}^{2}=2.5 M_{pl}^{2}$ and $m_{0}^{2}=0.095 M_{pl}^{2}$Pawlowski:2023dda.
• Figure 3: The graphs illustrate the possible event horizons $r_{h}$ with respect to variety values of $M$ and $S_{0}$. We used $m_{2}^{2}=2.5 M_{pl}^{2}$ and $m_{0}^{2}=0.095 M_{pl}^{2}$Pawlowski:2023dda.
• Figure 4: The graphs present the possible Hawking temperature $T (M, S_{0})$ with respect to variety values of $M$ and $S_{0}$. We used $m_{2}^{2}=2.5 M_{pl}^{2}$ and $m_{0}^{2}=0.095 M_{pl}^{2}$Pawlowski:2023dda.
• Figure 5: The graphs present the possible mass $M$ with respect to variety values of $r_{h}$ and $S_{0}$. We used $m_{2}^{2}=2.5 M_{pl}^{2}$ and $m_{0}^{2}=0.095 M_{pl}^{2}$Pawlowski:2023dda.