Can Galileons support Lorentzian wormholes?

Abstract

We discuss the possibility of constructing stable, static, spherically symmetric, asymptotically flat Lorentzian wormhole solutions in general relativity coupled to a generalized Galileon field π. Assuming that the Minkowski space–time is obtained at ∂_π = 0, we find that there is tension between the properties of the energy–momentum tensor required to support a wormhole (violation of the average null energy conditions) and stability of the Galileon perturbations about the putative solution (absence of ghosts and gradient instabilities). In three-dimensional space–time, this tension is strong enough to rule out wormholes with the above properties. In higher dimensions, including the most physically interesting case of four-dimensional space–time, wormholes, if any, must have fairly contrived shapes.