Gravitational-Wave Ringdown Through The Black Hole S-Matrix

After the merger of a binary black hole system, the remnant black hole undergoes free oscillations, emitting gravitational waves known as the ringdown signal. These ringdown waveforms contain multiple quasi-normal modes (QNMs), and it is expected that black hole spectroscopy—resolving these modes individually—will enable tests of gravity in the strong-field regime. However, extracting multiple QNMs from the ringdown requires fitting many parameters, which poses significant challenges for data analysis. In this talk, I will show that the interference pattern among QNMs exhibits universal features, which can be naturally described in terms of the black hole S-matrix or greybody factors. The black hole S-matrix, in particular, provides a compact characterization of the excitation and interference of many QNMs using only a few parameters, especially when the ringdown is sourced instantaneously. In this sense, the black hole S-matrix may be regarded as encoding the universal features of black hole QNM excitations.