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

TL;DR

This paper proves that within effective field theories, perturbative constructions of traversable wormholes near certain black holes are impossible due to symmetry constraints, highlighting the need for new ingredients or less symmetric black holes.

Contribution

It establishes no-go theorems showing perturbative wormhole solutions cannot be realized in effective field theories near specific black hole geometries.

Findings

Perturbative wormholes are forbidden in near-horizon geometries of Reissner-Nordstr"{o}m and Myers-Perry black holes.

Enhanced symmetries constrain the energy-momentum tensor, preventing wormhole formation.

Realizing traversable wormholes requires new ingredients or less symmetric black holes.

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.