Wheeler-DeWitt Equation for Black Hole Interiors in Asymptotically Safe Gravity

TL;DR

This paper investigates the Wheeler-DeWitt equation within asymptotically safe gravity, revealing that quantum effects can suppress singularities in black hole interiors, with classical solutions largely unaffected by scale-dependent couplings.

Contribution

It derives and analyzes the Wheeler-DeWitt equation incorporating scale-dependent gravitational couplings, showing quantum effects suppress singularities regardless of the RG scale identification.

Findings

Quantum behavior suppresses singularity formation in the ultraviolet regime.

Classical solutions remain unaffected by the running of Newton's constant.

Running of the cosmological constant influences classical solutions.

Abstract

In this work, we analyze the Wheeler-DeWitt equation with scale-dependent gravitational couplings within the framework of asymptotically safe gravity. In the Hamiltonian formulation based on a renormalization-group improved Einstein-Hilbert action, the consistency of the theory and the Poisson algebra of constraints have been clarified. Within this framework, we show that, despite the explicit scale dependence of Newton's constant, the classical solutions are generically unaffected by the running of the coupling. We then derive the Wheeler-DeWitt equation incorporating the scale dependence of the gravitational couplings and analyze its solutions in the minisuperspace framework. In the classical limit, while the scale dependence of Newton's constant does not affect the classical behavior, the running of the cosmological constant can contribute to the classical solutions. Moreover, we show that the quantum behavior in the ultraviolet regime acts toward suppressing singularity formation in all cases, independently of how the renormalization-group scale is identified with spacetime coordinates and of the relative magnitudes of the ultraviolet fixed points of the running Newton's constant and cosmological constant.