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

TL;DR

This paper develops a systematic approach to incorporate renormalization-group effects into spherically symmetric black-hole spacetimes, maintaining second-order equations and connecting to Horndeski theories, thus broadening the understanding of quantum corrections in gravity.

Contribution

It introduces a formalism for RG-improvement of black-hole spacetimes using two-dimensional Horndeski theories, capturing higher-curvature effects while preserving second-order field equations.

Findings

Derived static RG-improved black-hole solutions with radius-dependent gravitational coupling.

Connected RG-improvement procedures to two-dimensional Horndeski theories.

Clarified differences when implementing RG-improvement at various levels.

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.