The thesis will study theoretical aspects and symmetries of black hole perturbation theory, with applications to future gravitational-wave observations.

Black holes are notoriously the simplest macroscopic objects in the universe, uniquely determined by their mass and spin. Their simplicity stems from (hidden) symmetries in general relativity, which strongly constrain their perturbations and how they respond when they interact with an external environment. One example is the well-known fact that the static tidal deformability—a.k.a. the Love numbers—of (asymptotically flat) black holes in general relativity is exactly vanishing, as opposed to other types of compact objects like neutron stars, or black holes in higher-dimensional spacetimes. The tidal Love numbers are important because they offer insights into the gravitational behavior and the body’s internal structure. For a neutron star, the tidal deformability is tightly related to the object’s equation of state. In the case of black holes, the Love numbers depend on the physics at the horizon, and can be used to access and test the fundamental properties of gravity in the strong-field regime. 

The first main direction of the thesis we will be the study of the tidal deformability and Love numbers of black holes in general relativity, with particular focus on: non-linear tidal response of black holes, symmetry properties of gravitational effective field theories, non-static response.

The second direction will focus on general non-linear effects in black hole perturbation theory. Applications include: quasi-normal modes and ringdown, stability of black holes, turbulence phenomena.