Running Newton Coupling, Scale Identification and Black Hole Thermodynamics

TL;DR

This paper proposes using the first law of thermodynamics to identify the energy scale for the quantum-corrected Newton coupling in black hole solutions, leading to a universal quantum entropy formula consistent with classical results.

Contribution

It introduces a thermodynamics-based principle for scale identification in quantum black holes, deriving a universal quantum entropy formula that aligns with classical entropy.

Findings

Newton coupling depends on the horizon area

Universal quantum entropy formula derived

Consistency with Bekenstein-Hawking entropy

Abstract

We discuss the quantum improvement of black hole solutions in the context of asymptotic safety. The Newton coupling in this formulation depends on an energy scale, which must be identified with some length scale in order to study physical consequences to black holes. However, no physical principle has so far been known for the identification. Here we propose that the consistency of the first law of thermodynamics is the principle that should determine physically sensible scale identification, at least close to the horizon. We show that this leads to a natural solution that the Newton coupling should be a function of the horizon area and find a universal formula for the quantum entropy, which agrees with the standard Bekenstein-Hawking entropy for constant Newton coupling, for Kerr black holes and other higher-dimensional black holes. This suggests that the Newton coupling is a function of the area near the horizon, and also away to infinity, where the quantum effects may not be so important.