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

Abstract

We reformulate the construction of wormhole solutions as perturbations around near-horizon geometries of near-extremal Reissner-Nordstr\"{o}m 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-Nordstr\"{o}m 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.