Exploring nonlinear gravitational waves in Horndeski theory

In the fully nonlinear regime, gravitational waves can reveal drastic new phenomenology absent in the linearized theory. In this talk, I will review the role of disformal field redefinition to explore both the theories space and the solution space of modified gravity theories (focusing on scalar-tensor gravity). I shall first comment on the effect of disformal transformations on the Petrov type of a given geometry and use this opportunity to discuss how this can guide us in the construction of new exact solutions in scalar-tensor theories. Then, I will show how disformal field redefinition can the properties of a congruence of geodesics and in particular how they can generate disformal gravitational waves at the fully nonlinear level. I will illustrate this by presenting a new exact radiative solution in Horndeski gravity describing a scalar pulse. Analyzing this new radiative solution will show that in such higher order scalar-tensor theory, shear can be generated by a purely (time-dependent) scalar monopole, a feature which only emerge at the fully non-perturbative level and descends from the scalar-tensor mixing inbuilt in Horndeski gravity