General constraints on Horndeski wormhole throats

In this work, we consider the full Horndeski Lagrangian applied to wormhole geometries and present the full gravitational field equations. We analyze the general constraints imposed by the flaring-out conditions at the wormhole throat and consider a plethora of specific subclasses of the Homdeski Lagrangian, namely, quintessence and phantom fields, k-essence, scalar-tensor theories, covariant Galileons, nonminimal kinetic coupling, kinetic gravity braiding, and the scalar-tensor representation of Gauss-Bonnet couplings, among others. The generic constraints analyzed in this work serve as a consistency check of the main solutions obtained in the literature and draw out new avenues of research in considering applications of specific subclasses of the Horndeski theory to wormhole physics.