A classification of admissible energy density profiles with bounded Kretschmann scalar yields a unified framework for regular static spherically symmetric spacetimes satisfying the weak energy condition, recovering known models and producing new families with hypergeometric and other closed forms.
Effective geometrodynamics for renormalization-group improved black-hole spacetimes in spherical symmetry
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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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2026 7representative citing papers
Higher-order terms in an infinite tower of higher-derivative gravity regularize a 5D Proca-Maxwell system, creating frozen regular cores that mimic extremal black holes and satisfy all energy conditions.
All integrable 2D Horndeski theories (and thus many regular black-hole metrics) arise as spherical reductions of pure d≥4 gravities, which the paper terms quasi-topological.
Charged Bardeen and Hayward metrics become singular under deformed Einstein–Maxwell equations; more stringent regularity conditions are derived and improved regular charged metrics are constructed.
Dynamical black-hole-to-white-hole transitions require a violation of the null convergence condition for the trapped region to disappear and the anti-trapped region to form.
An off-shell Hessian criterion H = S'_W(r_h) T'(r_h) governs thermodynamic stability of higher-curvature black holes, recovering the temperature-slope rule on physical branches and producing mean-field critical exponents.
A unified framework links the generating function for static black holes satisfying g_tt g_rr=-1 in extended quasi-topological gravity to thermodynamic mass and Wald entropy via an effective 2D dilaton theory.
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$g_{tt}g_{rr} =-1$ black hole thermodynamics in extended quasi-topological gravity
A unified framework links the generating function for static black holes satisfying g_tt g_rr=-1 in extended quasi-topological gravity to thermodynamic mass and Wald entropy via an effective 2D dilaton theory.