Traversable wormholes in beyond Horndeski theories

Abstract

We construct a large class of explicit, asymptotically flat and regular wormhole solutions in higher order scalar tensor theories. The solutions are vacuum solutions of scalar tensor theory and no matter (exotic or regular) is introduced in order to support them. They are constructed via a general disformal transformation of a seed black hole solution. The seed solutions belong to a particular Horndeski theory which requires the presence of all extended Galileons and has a higher dimensional Lovelock origin. As a result, the resulting wormholes are always solutions of general beyond Horndeski theory. The particular class of wormholes we study are parametrised by their ADM mass and two coupling constants of the theory, one related to their higher dimensional Lovelock origin and one to the disformal transformation itself. The latter of the coupling constants affects the throat size of the wormhole solutions, thus giving them a compact or non-compact nature, as well as their properties.

Compact objects of spherical symmetry in beyond Horndeski theories

“…As it was shown in [64], one can obtain a beyond-Horndeski wormhole solution starting from a Horndeski black-hole solution. The seed solution found by Lu and Pang [55] (see also [56,57]) is described by the following Horndeski theory functions…”

“…The independent field equations for this symmetry can be obtained in all generality. They first appeared in the appendix of [41] and later presented in [64] with minor corrections.…”

“…There are numerous possibilities for the choice of Z = Z(X) which in fact give different types of black hole, wormhole or singular solutions. For a start if Z = Z(X) is infinite at a particular finite radius r = r T (which is not a zero of h and f ) then r = r T is a possible wormhole throat (see [64]). But it is now easy to see that since X is only function of r, according to (3.1), Z can only be a function of r and crucially not of the metric functions…”

“…In a recent publication [64], such techniques were used to construct a traversable regular wormhole solution (see also [82,83]). Let us re-visit this construction here with the benefit of our simplified field equations (2.6)-(2.8).…”

“…Let us re-visit this construction here with the benefit of our simplified field equations (2.6)-(2.8). Following [64], by barred quantities we will be noting the seed "known" Horndeski solution. As such we have φ, h, f and of course X = − 1 2 f φ 2 for some specific set of coupling functions { Ḡi } in Horndeski theory.…”