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 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''.

4 pages, revtex4; V2: discussion refined and strengthened in view of referee comments, no changes in physics conclusions. To appear in Physical Review Letters