WI Seminar with Marica Minucci

Abstract: Late-time gravitational-wave signals from black hole mergers are dominated by quasinormal modes (QNMs), damped oscillations whose complex frequencies depend only on the final black hole’s mass and spin. These modes provide a distinctive spectral signature of the remnant. To interpret these signals beyond linear theory, we need tools to describe QNM interactions. While ringdown waveforms are well approximated by linear superpositions, Kerr QNMs are not orthogonal and do not form a complete basis in the usual sense. Moreover, when defined on Cauchy hypersurfaces, their mode functions are singular at both the horizon and spatial infinity.
I will present bilinear forms constructed from conserved currents and symmetry operators that act as inner-product analogues for gravitational perturbations on hyperboloidal foliations. Using Schwarzschild spacetime as a model, I will outline their main properties and potential use for studying nonlinear mode mixing.