Scalar fields, energy conditions, and traversable wormholes

TL;DR

This paper explores how non-minimally coupled scalar fields can violate energy conditions, leading to classical solutions that include traversable wormholes, which are consistent with current physical constraints.

Contribution

It derives and analyzes static, spherically symmetric solutions showing traversable wormholes supported by non-minimally coupled scalar fields with positive curvature coupling.

Findings

Non-minimally coupled scalars can violate all standard energy conditions.

Traversable wormholes exist for every positive coupling xi>0.

Scalar fields must reach trans-Planckian values in these solutions.

Abstract

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.