Dhost theories as disformal gravity: from black holes to radiative spacetimes

Abstract This manuscript gathers and reviews part of our work focusing on the exploration of modified theories of gravity known as degenerate higher order scalar-tensor (DHOST) theories. It focuses on the construction of exact solutions describing both black holes and radiative spacetimes. After motivating the need for alternatives theories of gravity beyond general relativity, we discuss in more details the long terms objectives of this research program. The first one is to characterize both the theory and some sectors of the solution space of DHOST gravity. The second one is to provide concrete and exact solutions of the DHOST field equations describing compact objects, in particular black holes, that can be used to confront DHOST theories to current and future observations in the strong field regime. A key tool towards these two objectives is the concept of disformal field redefinition (DFR) which plays a central role in this exploration. We start be reviewing the structure of the DHOST theory space, the notion of degeneracy conditions and the stability of these degeneracy classes under DFR. Then we review 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 sections are devoted to a review of the disformal solution generating map, the subtle role of matter coupling and how it can be used to construct new hairy black holes solutions. The case of spherically symmetric solutions, axi-symmetric but non-rotating solutions, and finally rotating solutions are discussed, underlining the advantages and the limitations of this approach. A brief review of the rotating black holes solutions found so far in this context is followed by the 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. 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.