Running Newton Coupling, Scale Identification and Black Hole Thermodynamics

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.

14 pages, v2: various elaborations, 2 refs. added

References in corpus (5)

• Spacetime Structure of an Evaporating Black Hole in Quantum Gravity
• Instabilities of Black Strings and Branes
• Quantum Gravity Effects in the Kerr Spacetime
• Quantum improved charged black holes
• Stresses and Strains in the First Law for Kaluza-Klein Black Holes

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• Effective geometrodynamics for renormalization-group improved black-hole spacetimes in spherical symmetry
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• GUP Effective Metric Without GUP: Implications for the Sign of GUP Parameter and Quantum Bounce
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• Do Black Holes With Generalized Entropy Violate Bekenstein Bound?
• Equivalence of scalar-tensor theories and scale-dependent gravity
• Shadow of rotating black holes with consistent thermodynamics
• Sign Switching Dark Energy from a Running Barrow Entropy