RG-improved black hole spacetimes with scale-dependent gravitational coupling are derived as vacuum solutions to 2D Horndeski master field equations, embedding prior works and exposing implementation discrepancies.
Renormalization group improved gravitational actions: A Brans-Dicke approach
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abstract
A new framework for exploiting information about the renormalization group (RG) behavior of gravity in a dynamical context is discussed. The Einstein-Hilbert action is RG-improved by replacing Newton's constant and the cosmological constant by scalar functions in the corresponding Lagrangian density. The position dependence of $G$ and $\Lambda$ is governed by a RG equation together with an appropriate identification of RG scales with points in spacetime. The dynamics of the fields $G$ and $\Lambda$ does not admit a Lagrangian description in general. Within the Lagrangian formalism for the gravitational field they have the status of externally prescribed ``background'' fields. The metric satisfies an effective Einstein equation similar to that of Brans-Dicke theory. Its consistency imposes severe constraints on allowed backgrounds. In the new RG-framework, $G$ and $\Lambda$ carry energy and momentum. It is tested in the setting of homogeneous-isotropic cosmology and is compared to alternative approaches where the fields $G$ and $\Lambda$ do not carry gravitating 4-momentum. The fixed point regime of the underlying RG flow is studied in detail.
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gr-qc 3years
2026 3verdicts
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In asymptotically safe gravity, radiation-filled Bianchi-I cosmologies show quantum corrections that soften anisotropy, while magnetic fields lead to persistent Kasner anisotropy without Lambda but isotropic de Sitter decay with nonzero Lambda.
Thermodynamic consistency for quantum-improved Reissner-Nordström black holes permits arbitrary radial dependence in both Newton and electromagnetic couplings, while equation-action consistency requires an extra quantum energy-momentum tensor and specific properties for the Newton coupling.
citing papers explorer
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Effective geometrodynamics for renormalization-group improved black-hole spacetimes in spherical symmetry
RG-improved black hole spacetimes with scale-dependent gravitational coupling are derived as vacuum solutions to 2D Horndeski master field equations, embedding prior works and exposing implementation discrepancies.
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Bianchi-I Cosmology with Radiation in Asymptotically Safe Gravity
In asymptotically safe gravity, radiation-filled Bianchi-I cosmologies show quantum corrections that soften anisotropy, while magnetic fields lead to persistent Kasner anisotropy without Lambda but isotropic de Sitter decay with nonzero Lambda.
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Consistency in the Quantum-Improved Charged Black Holes
Thermodynamic consistency for quantum-improved Reissner-Nordström black holes permits arbitrary radial dependence in both Newton and electromagnetic couplings, while equation-action consistency requires an extra quantum energy-momentum tensor and specific properties for the Newton coupling.