Effective Quantum Spacetimes from Functional Renormalization Group (2410.16866v2)

Abstract: Using the Functional Renormalization Group approach we construct effective quantum spacetime geometries by self-consistently deforming the classical Schwarzschild-de Sitter black-hole solution. This involves studying how quantum corrections, driven by the running of the Newton's and cosmological constants modify the solution across the infrared and ultraviolet regimes. We show that these quantum modifications replace the Schwarzschild singularity with a milder conical one. Moreover, two new features emerge in the ultraviolet regime. First, we identify a phase transition between Anti-de Sitter/de Sitter spacetime occurring when the object's mass exceeds a first critical threshold. Second, we predict the formation of horizons once the object's mass exceeds a second threshold. Both thresholds are of the order of the Planck mass. Finally, we investigate the role of the anomalous dimension in the conformal sector of the theory.