Probing new physics on the horizon of black holes with gravitational waves

Black holes are the most compact objects in the Universe. According to general relativity, black holes have a horizon that hides a singularity where Einstein’s theory breaks down. Recently, gravitational waves opened the possibility to probe the existence of horizons and investigate the nature of compact objects. This is of particular interest given some quantum-gravity models which predict the presence of horizonless and singularity-free compact objects. Such exotic compact objects can emit a different gravitational-wave signal relative to the black hole case. In this thesis, we analyze the stability of horizonless compact objects, and derive a generic framework to compute their characteristic oscillation frequencies. We provide an analytical, physically- motivated template to search for the gravitational-wave echoes emitted by these objects in the late-time postmerger signal. Finally, we infer how extreme mass-ratio inspirals observable by future gravitational-wave detectors will allow for model-independent tests of the black hole paradigm