DHOST theories as disformal gravity: From black holes to radiative spacetimes

This manuscript reviews the construction of exact solutions describing both (rotating) black holes and non-linear radiative spacetimes in the context of degenerate higher order scalar-tensor (DHOST) theories. We start be reviewing the structure of the DHOST theory space, the notion of degeneracy conditions and the stability of these degeneracy classes under disformal field redefinition (DFR). Then we discuss several key notions related to stationary and axi-symmetric black holes, and in particular the no-hair theorems derived in GR and in its scalar-tensor extensions. The rest of the chapters are devoted to the disformal solution generating map use to construct new hairy black holes solutions. A brief review of the rotating black holes solutions found so far in this context and a detailed description of the disformed Kerr black hole, we further comment on on-going efforts to construct rotating black hole solutions mimicking the closest the Kerr geometry. Then, we discuss how DFR affects the algebraic properties of a gravitational field and in particular its Petrov type. This provides a first systematic characterization of this effect, paving the road for constructing new solutions with a fixed Petrov type. Finally, we review more recent works aiming at characterizing the effect of a DFR on non-linear radiative geometries. We derive the general conditions for the generation of disformal tensorial gravitational wave and we study in detail a concrete example in DHOST gravity describing the new radiative effect induced by a time-dependent scalar monopoly in such higher-order theory. While most of the material presented here is a re-organized and augmented version of our published works, we have included new results and also new proposals to construct phenomenologically interesting solutions. This manuscript can be used as a review on the construction of exact solutions in DHOST gravity.