Wormholes as perturbations of near-horizon black hole geometries: no-go theorems within effective field theories

TL;DR

The paper investigates whether traversable wormholes can be realized as perturbative corrections to highly symmetric near-horizon geometries of black holes within an effective field theory (EFT) framework. By reformulating wormhole construction as perturbations around the near-horizon AdS$^{2}\times$S$^{2}$ geometry of near-extremal RN and equal-angular-momenta MP black holes in 4D and 5D, the authors derive no-go theorems: purely covariant higher-derivative corrections in EFT cannot generate a traversable throat, due to the strong symmetry constraints on the effective energy–momentum tensor at the throat. The RN analysis shows that at first order, and then at higher orders, the throat flare-out condition cannot be satisfied; the MP analysis yields the same obstruction under matching to the exterior near-horizon geometry. The results suggest that realizing traversable wormholes within this EFT framework would require either non-EFT ingredients, such as Casimir energy, or black holes with reduced symmetry, highlighting the role of quantum effects or symmetry breaking in enabling such geometries.

Abstract

We reformulate the construction of wormhole solutions as perturbations around near-horizon geometries of near-extremal Reissner-Nordström black holes in four dimensions and equal-angular-momenta Myers-Perry black holes in five dimensions. When the negative Casimir energy is taken as the source, this framework reduces to the Maldacena-Milekhin-Popov construction for magnetically charged wormholes. We then show that, in contrast, such perturbative constructions cannot be realized within the effective field theory approach to higher-derivative corrections. Remarkably, this conclusion holds irrespective of the specific form of the correction terms. The key observation is that the enhanced symmetries in the near-horizon region severely constrain the effective energy-momentum tensor near the throat. This prevents the formation of the traversable throat structure. Our analysis therefore establishes no-go theorems: traversable wormholes cannot arise perturbatively from Reissner-Nordström or Myers-Perry black holes in an effective field theory approach. Their realization would require either new ingredients, such as Casimir energy, or black holes with reduced symmetry.