Quasi-normal Modes and Stability of the Solutions

The stability of solutions against linear perturbations is one of the most important properties to investigate. An unstable solution in general will be in a time-evolving state and, if the time scales of this evolution are much shorter than the ones generally present in Astrophysics, the probability of detecting it could be effectively zero. The phase diagram of solutions of quadratic gravity and the knowledge of their global properties are then only the starting point for the analysis of these solutions in a physical context. In this chapter, we study the evolution of linear perturbations of quadratic gravity and scale-invariant gravity solutions, with a special focus on black hole solutions.