Towards wormhole beyond Horndeski

We address the issue of whether a no-go theorem for static, spherically symmetric wormholes, proven in Horndeski theories, can be circumvented by going beyond Horndeski. We show that the ghost instabilities which are at the heart of the no-go theorem, can indeed be avoided. The wormhole solutions with the latter property are, however, strongly fine tuned, and hence it is likely that they are unstable. Furthermore, it remains unclear whether these solutions have other pathologies, like gradient instabilities along angular and radial directions. (authors)