Traversable wormholes with arbitrarily small energy condition violations

Abstract

Traversable wormholes necessarily require violations of the averaged null energy condition; this being the definition of “exotic matter”. However, the theorems which guarantee the energy condi- tion violation are remarkably silent when it comes to making quantitative statements regarding the “total amount” of energy condition violating matter in the spacetime. We develop a suitable mea- sure for quantifying this notion, and demonstrate the existence of spacetime geometries containing traversable wormholes that are supported by arbitrarily small quantities of “exotic matter”.