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arXiv · 2601.17115

Effective geometrodynamics for renormalization-group improved black-hole spacetimes in spherical symmetry

Johanna Borissova·Raúl Carballo-Rubio
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Abstract

We consider the spherically reduced Einstein-Hilbert action, Einstein field equations and Schwarzschild spacetime modified by a renormalization-group (RG) scale-dependent gravitational Newton coupling, and present a systematic and operational approach to such an RG-improvement. The master field equations for spherically symmetric gravitational fields, recently constructed from two-dimensional Horndeski theory, allow us to retain partial contributions from higher-curvature truncations of the effective action, while preserving the second-order nature of the resulting field equations. Static RG-improved black-hole spacetimes with an effective gravitational coupling depending on the areal radius and the Misner-Sharp mass are derived as vacuum solutions to these master field equations, and are thereby identified as solutions to generally covariant two-dimensional Horndeski theories. We discuss explicitly the embedding of previous key works on RG-improvement into the newly developed formalism to illustrate its broad range of applicability. This formalism moreover allows us to establish explicitly the discrepancies in the outcomes of RG-improvement when implemented at the level of the action, in the field equations, or in the Schwarzschild solution.

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Johanna Borissova, Raúl Carballo-Rubio. 2026-01-23. Effective geometrodynamics for renormalization-group improved black-hole spacetimes in spherical symmetry. https://doi.org/10.1088/1475-7516%2F2026%2F05%2F023

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