Scalar fields, energy conditions and traversable wormholes

We describe the different possibilities that a simple and apparently quite harmless classical scalar field theory provides to violate the energy conditions. We demonstrate that a non-minimally coupled scalar field with a positive curvature coupling ξ>0 can easily violate all the standard energy conditions, up to and including the averaged null energy condition (ANEC). Indeed, this violation of the ANEC suggests the possible existence of traversable wormholes supported by non-minimally coupled scalars. To investigate this possibility we derive the classical solutions for gravity plus a general (arbitrary ξ) massless non-minimally coupled scalar field, restricting attention to the static and spherically symmetric configurations. Among these classical solutions we find an entire branch of traversable wormholes for every ξ>0. (This includes and generalizes the case of conformal coupling ξ = (1/6) we considered in 1999 Phys. Lett. B 466 127-34.) For these traversable wormholes to exist we demonstrate that the scalar field must reach trans-Planckian values somewhere in the geometry. We discuss how this can be accommodated within the current state of the art regarding scalar fields in modern theoretical physics. We emphasize that these scalar field theories, and the traversable wormhole solutions we derive, are compatible with all known experimental constraints from both particle physics and gravity.