Symmetries of black hole perturbations

The direct detection of gravitational waves has marked the dawn of the era of gravitational-wave astronomy. With an ever increasing number of observed black hole mergers and with the possibility of precise measurements achievable with third-generation and space-based detectors, gravitational-wave astronomy is providing us with a unique opportunity to test general relativity in the strong-field regime. In order to understand how gravity works at the fundamental level and explain some still unsolved mysteries about black holes and compact objects, symmetries play a special role. Symmetries allow, e.g., to make robust and model-independent predictions for the observables, and constrain broad classes of theories beyond general relativity. 
After a short review of black hole perturbation theory, I will discuss properties of perturbations around Schwarzschild black holes. I will discuss, in particular, the implications of symmetries at the level of the observables. These include the quasi-normal mode spectrum and the static response of black holes, a.k.a. the Love numbers. If time permits, I will introduce an effective field theory for perturbations around “hairy” black holes and discuss how gravitational-wave observations could be used to constrain the couplings of the operators in the theory.