Orateur
Description
Exact solutions are crucial in our understanding of the gravitational field both for black hole and gravitational waves. In this talk, I will review the efforts in constructing exact solutions in modified gravity, focusing on the case of Degenerate Higher Order Scalar Tensor (DHOST) theories. I will underline the limitations we face so far to explore and organize the solution space of these theories, in particular the sectors relevant for the description of compact objects and gravitational waves phenomenology. In the first part, I will discuss the most recent no-hair theorem for DHOST and how suitable disformal solutions by pass its assumptions. Then, I shall discuss the key theorems of general relativity, in particular the Goldberg Sachs theorem, which single out algebraically special solutions. To that end, I will review the Newman-Penrose formalism and the Petrov classification which are key to derive these theorems. I will further show how the Petrov type allows one to identify suitable solutions with hidden symmetries. Finally, if time allows it, I will discuss the case of non-linear gravitational waves and how one provide general conditions, using the Newman-Penrose formalism, to generate tensorial gravitational waves from a disformal transformation. The main goal of the presentation is to review the key ruling structures of the solution space of general relativity and see how we can import or adapt them to study the solution space of alternatives theories of gravity.
