Gravitational wave signatures of scalarized black holes and horizonless compact objects

Black holes are among the simplest objects in the universe, yet they serve as one of the most powerful testbeds for probing some of the deepest puzzles in physics, such as the curvature singularity, the information loss paradox and other fundamental challenges within general relativity. These unresolved issues motivated the investigation of alternative models of compact objects. Among the various proposals, the Fuzzball program stands out as one of the most promising top-down approaches to resolving these problems in one coherent picture, as it describes the black hole as an ensemble of smooth and horizonless geometries representing its microstates with the same mass and charge. The flourishing field of gravitational waves research provides an excellent avenue for investigating the phenomenology of these objects. This thesis focuses on the study of toy models whose simplified yet physically motivated solutions, involving gravity coupled with additional degrees of freedom, effectively capture key properties of Fuzzballs. We investigate the perturbative response of these objects by computing their oscillatory modes and highlighting the presence of echo patterns in the ringdown signal. Moreover, we analyze extreme-mass-ratio inspirals as a promising probe to differentiate classical black holes from horizonless compact objects in these toy models.