Stealth Ellis Wormholes In Horndeski theories

TL;DR

This paper demonstrates that Ellis wormholes can exist as stealth solutions in generalized Horndeski theories, supported by higher derivative scalar couplings, and introduces mechanisms to give these wormholes an effective mass.

Contribution

It shows Ellis wormholes are stealth solutions in Horndeski theories with higher derivatives and proposes methods to assign them an effective ADM mass.

Findings

Ellis wormholes are supported by non-trivial scalar couplings in Horndeski theories.

The wormholes can be dressed with an effective mass via conformal transformations or scalarization.

The solutions do not back-react on the spacetime metric, confirming their stealth nature.

Abstract

In this work we are revisiting the well studied Ellis wormhole solution in a generalized Horndeski theory motivated from the Kaluza-Klein compactification procedure of the more fundamental higher dimensional Lovelock gravity. We show that the Ellis wormhole is analytically supported by a gravitational theory with a non-trivial coupling to the Gauss-Bonnet term and we expand upon this notion by introducing higher derivative contributions of the scalar field. The extension of the gravitational theory does not yield any back-reacting component on the spacetime metric, which establishes the Ellis wormhole as a stealth solution in the generalized framework. We propose two simple mechanisms that dress the wormhole with an effective ADM mass. The first procedure is related to a conformal transformation of the metric which maps the theory to another Horndeski subclass, while the second one is inspired by the spontaneous scalarization effect on black holes.