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

TL;DR

This paper investigates the thermodynamics and entanglement properties of black holes within asymptotically safe quantum gravity, demonstrating how island contributions resolve the information paradox and ensure unitary evolution.

Contribution

It introduces a novel analysis of entanglement islands in asymptotically safe quantum gravity, showing how they resolve the black hole information paradox and establish consistent thermodynamics.

Findings

Radiation entropy saturates at the Bekenstein-Hawking entropy at late times.

Including islands resolves the information paradox and supports unitarity.

The temperature behavior indicates a phase transition near evaporation endpoint.

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.