Numerically solved, but not yet understood: recent advancements in the gravitational twobody problem

The study of black holes' resonant excitation and their subsequent relaxation ("Black Hole Spectroscopy") is a fundamental tool to observationally investigate gravity in its most dynamical and violent regime. Recently, the unprecedented loudness of the gravitational wave signal GW250114 allowed us to exploit spectroscopic techniques to achieve the first accurate verification of two long-standing predictions of general relativity: Hawking's Area Law and the Kerr nature of the source.

The physical process behind these signals, namely the end state of the gravitational two-body problem, has been numerically solved twenty years ago. However, despite the striking simplicity of black holes, and decades of developments in classical perturbation theory, a first-principles understanding of the dynamical stage in which two black holes fuse together (the "merger" regime), is still lacking.

Such ignorance prevents even more exciting observational explorations, and the construction of signal models in richer scenarios. In this seminar I will detail recent breakthroughs in this direction, and their potential to advance our understanding of gravity, searches for new physics, and to harvest the full potential of next-generation detectors in achieving high-precision measurements.