Scalarfields, energy conditions and traversable wormholes

Abstract

We describe the different possibilities that a simple and apparentlyquite harmless classical scalar field theory provides to violate theenergy conditions. We demonstrate that a non-minimally coupled scalarfield with a positive curvature coupling ξ>0 can easily violateall the standard energy conditions, up to and including the averagednull energy condition (ANEC). Indeed, this violation of the ANECsuggests the possible existence of traversable wormholes supported bynon-minimally coupled scalars. To investigate this possibility wederive the classical solutions for gravity plus a general (arbitraryξ) massless non-minimally coupled scalar field, restrictingattention to the static and spherically symmetric configurations.Among these classical solutions we find an entire branch oftraversable wormholes for every ξ>0. (This includes andgeneralizes the case of conformal coupling ξ = (1/6) weconsidered in1999 Phys. Lett. B 466 127-34.) For these traversablewormholes to exist we demonstrate that the scalar field must reachtrans-Planckian values somewhere in the geometry. We discuss how thiscan be accommodated within the current state of the art regardingscalar fields in modern theoretical physics. We emphasize that thesescalar field theories, and the traversable wormhole solutions wederive, are compatible with all known experimental constraints fromboth particle physics and gravity.