Higher curvature corrections to the black hole Wheeler-DeWitt equation and the annihilation to nothing scenario

We revisit Yeom’s annihilation-to-nothing scenario using a modified Wheeler-DeWitt (WDW) equation incorporating higher-curvature corrections. We show that, once these corrections are taken into account, the WDW wave function exhibits severe divergences arising from contributions near the classical singularity. These divergences indicate that the low-energy effective field theory (EFT) description breaks down in this regime. Given that general relativity (GR) itself is merely a low-energy effective field theory (EFT) of an underlying ultraviolet (UV) theory, our results suggest that any attempted resolution of the black hole singularity cannot be reliably discussed within the EFT framework. Our analysis does not contradict Yeom’s conjecture, but emphasizes that the annihilation-to-nothing scenario should be discussed within a UV-complete theoretical framework. It further clarifies that any genuine resolution of the singularity necessarily requires a framework capable of appropriately describing ultraviolet physics, such as degrees of freedom beyond those captured by GR or dynamics consistently defined up to arbitrarily high energy scales.

💡 Research Summary

The paper revisits the “annihilation‑to‑nothing” proposal originally put forward by Yeom and collaborators, which suggests that two opposite‑time‑arrow branches of a black‑hole interior wave function cancel each other inside the horizon, thereby removing the classical singularity. The authors adopt a modern effective‑field‑theory (EFT) viewpoint, treating general relativity (GR) as the leading term of a low‑energy expansion that inevitably receives higher‑curvature corrections at energies approaching the Planck scale.

Starting from the D‑dimensional Einstein–Hilbert action, they perform a minisuperspace reduction inside the horizon using the Kantowski–Sachs metric. By defining the variables (X=\alpha) and (Y=\alpha+(D-3)\beta), the Hamiltonian constraint reduces to a two‑dimensional Wheeler‑DeWitt (WDW) equation \