TITLE: Testing the gravitational sector with black hole perturbations

ABSTRACT: In this talk, I will introduce an effective field theory (EFT) for perturbations around spherically symmetric spacetimes with a non-trivial scalar field profile. I will then apply this framework to study quasi-normal modes of static black holes with a scalar hair. I will argue that ``hairy'' solutions provide the most minimal yet interesting modifications of the quasinormal spectrum of Schwarzschild black holes. Assuming that the deviation of the background from Schwarzschild is small, I will use a WKB approximation to introduce the notion of "light ring expansion". This approximation is analogous to the slow-roll expansion used for inflation, and it allows us to express the quasinormal mode spectrum in terms of a small number of model-independent parameters to be constrained by observations. This is the first step towards an EFT framework for placing model-independent constraints on the gravitational sector based on the ringdown phase of gravitational wave events.