Traversable wormholes with arbitrarily small energy condition violations

TL;DR

This paper introduces a measure to quantify the amount of exotic matter needed for traversable wormholes and demonstrates that such wormholes can exist with arbitrarily small energy condition violations.

Contribution

It provides a new quantitative measure for exotic matter and shows that traversable wormholes can be supported with minimal energy condition violations.

Findings

Existence of wormhole geometries with arbitrarily small exotic matter

Development of a measure for quantifying exotic matter

Implications for realistic wormhole construction

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 condition 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 measure for quantifying this notion, and demonstrate the existence of spacetime geometries containing traversable wormholes that are supported by arbitrarily small quantities of ``exotic matter''.