  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 xi>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 xi) 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 xi>0. (This includes and generalizes the case of conformal
coupling xi=1/6 we considered in Phys. Lett. B466 (1999) 127--134;
gr-qc/9908029) 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.
