Invariant Renormalization-Group improvement

TL;DR

This paper introduces a coordinate-independent method for applying Renormalization-Group improvement to black-hole spacetimes using curvature invariants, addressing limitations of previous coordinate-dependent approaches.

Contribution

It proposes a novel RG improvement technique based on curvature invariants, ensuring coordinate independence in quantum-corrected spacetime models.

Findings

RG improvement at the metric level is coordinate-dependent

Curvature invariant-based RG improvement is coordinate-independent

Application to black-hole spacetimes demonstrates the method's effectiveness

Abstract

Renormalization-Group (RG) improvement has been frequently applied to capture the effect of quantum corrections on cosmological and black-hole spacetimes. This work utilizes an algebraically complete set of curvature invariants to establish that: On the one hand, RG improvement at the level of the metric is coordinate-dependent. On the other hand, a newly proposed RG improvement at the level of curvature invariants is coordinate-independent. Spherically-symmetric and axially-symmetric black-hole spacetimes serve as physically relevant examples.