Can Galileons support Lorentzian wormholes?

TL;DR

This paper investigates whether stable Lorentzian wormholes can exist in General Relativity coupled with Galileon fields, finding significant theoretical constraints that largely prohibit their existence in 3D and make them highly contrived in higher dimensions.

Contribution

It demonstrates the incompatibility between the energy conditions needed for wormholes and the stability conditions of Galileon perturbations, ruling out simple wormhole solutions in 3D and constraining their shape in higher dimensions.

Findings

Wormholes in 3D are ruled out due to instability.

In 4D, wormholes can only exist with highly contrived shapes.

Energy condition violations conflict with Galileon stability requirements.

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 $\pi$. Assuming that Minkowski space-time is obtained at $\partial \pi =0$, we find that there is tension between the properties of the energy-momentum tensor required to support a wormhole (violation of average null energy conditions) and stability of the Galileon perturbations about the putative solution (absence of ghosts and gradient instabilities). In 3-dimensional space-time, this tension is strong enough to rule out wormholes with above properties. In higher dimensions, including the most physically interesting case of 4-dimensional space-time, wormholes, if any, must have fairly contrived shapes.