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