The chime of cosmic bells: nonlinear effects and new physics in the black hole ringdown

Gravitational waves offer a powerful tool to test the nature of gravity in the strong-field regime, where deviations from Einstein’s General Relativity may emerge. Black hole mergers, in particular, are ideal laboratories for such tests, as their dynamics and emitted radiation encode detailed information about the underlying gravitational theory. This thesis explores two complementary avenues for probing gravity with black hole binaries. The first part focuses on black hole solutions in scalar–tensor theories, which extend General Relativity by adding an extra scalar field. In this context, “no-hair” theorems usually forbid black holes from carrying scalar charge, but existing results cover only special cases. We generalize these theorems, proving that in the most general shift-symmetric scalar-tensor theory, stationary black holes cannot possess scalar charge — even in higher-dimensional spacetimes. We also identify situations where this result can be circumvented, such as when the scalar field evolves linearly in time or couples to specific curvature invariants. These exceptions are phenomenologically relevant, as they can lead to distinctive gravitational wave signatures like dipolar radiation, potentially detectable by current and future detectors. The second part of the thesis employs the black hole perturbation theory framework to study how subtle changes in BH properties affect their quasinormal mode spectrum—the characteristic “ringing” observed in the post-merger gravitational wave signal. We analyze scenarios where the black hole mass changes over time, such as the nonlinear self-absorption of gravitational radiation, finding shifts in quasinormal frequencies, possible instabilities, and non-zero tidal responses. We also develop a parametrized framework to describe generic small deviations from GR in the Teukolsky equation. We demonstrate how this approach can be applied to a broad range of physical scenarios. We finally assess the impact of incomplete ringdown modeling on parameter estimation for the space-based detector LISA, by incorporating multiple fundamental, overtone, and quadratic modes. In summary, the work refines theoretical constraints on black hole properties, highlights specific scenarios and conditions where deviations from GR could be observable, and outlines approaches that may help connect theoretical predictions with future GW measurements.