Effective geometrodynamics for renormalization-group improved black-hole spacetimes in spherical symmetry
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arXiv
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866917472906510336 |
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| author | Borissova, Johanna Carballo-Rubio, Raúl |
| author_facet | Borissova, Johanna Carballo-Rubio, Raúl |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_17115 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Effective geometrodynamics for renormalization-group improved black-hole spacetimes in spherical symmetry Borissova, Johanna Carballo-Rubio, Raúl General Relativity and Quantum Cosmology High Energy Physics - Theory 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. |
| title | Effective geometrodynamics for renormalization-group improved black-hole spacetimes in spherical symmetry |
| topic | General Relativity and Quantum Cosmology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2601.17115 |