Higher curvature corrections to the black hole Wheeler-DeWitt equation and the annihilation to nothing scenario
Takamasa Kanai
TL;DR
This work analyzes black hole interior singularities through the Wheeler–DeWitt framework by incorporating higher-curvature corrections within an effective field theory (EFT) of gravity. By performing both classical and quantum perturbative analyses of curvature-squared and curvature-cubed terms in a Kantowski–Sachs minisuperspace, the authors show that Yeom's annihilation-to-nothing scenario, which suggested singularity resolution at the GR level, does not survive EFT corrections. The results demonstrate that the WDW wave function does not vanish at the would-be singular point once UV-sensitive corrections are included, implying that true resolution requires UV-complete quantum gravity degrees of freedom beyond GR. The findings emphasize the limited domain of validity of the semiclassical EFT approach for singularity resolution and point toward nonperturbative UV frameworks such as loop quantum gravity or asymptotic safety as necessary to resolve black hole singularities in a physically consistent way.
Abstract
We revisit Yeom's annihilation-to-nothing scenario using a modified Wheeler-DeWitt (WDW) equation, incorporating higher curvature corrections. By taking these corrections into account, we show that singularity resolution does not occur within low-energy effective field theory (EFT). Since general relativity (GR) is itself only a low-energy EFT of an underlying ultraviolet (UV) theory, it is unlikely that true singularity resolution can emerge within its domain of validity. Our analysis does not contradict Yeom's conjecture but clarifies that any true resolution of the black hole singularity necessarily requires the inclusion of UV degrees of freedom beyond the scope of GR.