Maintaining a Wormhole with a Scalar Field

It is well known that it takes matter that violates the averaged weak energy condition to hold the throat of a wormhole open. The production of such “exotic” matter is usually discussed within the context of quantum field theory. In this paper I show that it is possible to produce the exotic matter required to hold a wormhole open classically. This is accomplished by coupling a scalar field to matter that satisfies the weak energy condition. The energy-momentum tensor of the scalar field and the matter separately satisfy the weak energy condition, but there exists an interaction energy-momentum tensor that does not. It is this interaction energy-momentum tensor that allows the wormhole to be maintained.