Ultraviolet Behavior of the Wheeler–DeWitt Equation in Horava–Lifshitz Gravity

We investigate the quantum structure of black hole interiors in Hořava–Lifshitz gravity by analyzing the Wheeler–DeWitt equation in minisuperspace. Focusing on the ultraviolet regime, where higher-order spatial curvature terms dominate, we derive analytical solutions in this UV limit for both the original Hořava–Lifshitz action and its analytically continued counterpart. We study their behavior near the event horizon and the classical singularity, with particular attention to the interpretation of the wave function in terms of the annihilation-to-nothing scenario proposed in general relativity. In this paper, we have considered cases in which the two-dimensional spatial section is spherical, planar, or hyperbolic, as well as models with positive, negative, or vanishing cosmological constant. In all cases, we find that the terms dominating in the ultraviolet regime, together with the effects of the running scaling parameter, act to suppress the annihilation-to-nothing behavior. These results suggest that, at least within the range explored in this study, the characteristic annihilationto-nothing behavior does not appear in the ultraviolet regime of Hořava–Lifshitz gravity, and provide a new perspective on the understanding of singularity resolution in quantum gravity.