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

In this work, we analyze the Wheeler–DeWitt equation with scale-dependent gravitational couplings within the framework of asymptotically safe gravity. The running couplings are treated as externally specified functions encoding renormalization-group information, rather than independent dynamical degrees of freedom. We formulate the Hamiltonian description starting from a renormalization-group–improved Einstein–Hilbert action and examine the resulting structure of the canonical constraints. The modification of the Poisson algebra reflects the presence of scale-dependent couplings and illustrates how ultraviolet information can influence the infrared canonical framework. Within a minisuperspace framework appropriate for black hole interiors, we derive the corresponding Wheeler–DeWitt equation and analyze its solutions. In the classical limit, under the assumptions adopted in this work, the running of Newton’s constant does not alter the structure of the classical singularity, which therefore remains unresolved at the classical level. By contrast, the scale dependence of the cosmological constant can affect certain aspects of the classical dynamics. At the quantum level, the ultraviolet behavior of the running couplings induces an effective potential structure in the Wheeler–DeWitt equation, leading to a suppression of the wave function in the vicinity of the classical singularity. This suppression arises for a broad class of scale-identification prescriptions considered here, suggesting that renormalization-group effects may contribute to the quantum mechanical softening of black hole singularities.