Conformally coupled theories and their deformed compact objects: from black holes, radiating spacetimes to eternal wormholes

We study a higher order conformally coupled scalar tensor theory endowed with a covariant geometric constraint relating the scalar curvature with the Gauss-Bonnet scalar. It is a particular Horndeski theory including a canonical kinetic term but without shift or parity symmetry for the scalar. The theory also stems from a Kaluza-Klein reduction of a well defined higher dimensional metric theory. Properties of an asymptotically flat spherically symmetric black hole are analyzed, and new slowly rotating and radiating extensions are found. Through disformal transformations of the static configurations, gravitating monopole-like solutions and eternal wormholes are presented. The latter are shown to extract from spacetime possible naked singularities, yielding completely regular and asymptotically flat spacetimes.