Marica Minucci - Conserved Currents and Bilinear Forms for Quasinormal Modes in the Hyperboloidal...

Описание: This lecture was part of the Workshop on "Hyperboloidal Foliations and their Application" held at the ESI January 12 to 16, 2026.

The late-time gravitational-wave signal from a binary black hole merger is dominated by quasinormal ringing, a spectrum of damped oscillations whose complex frequencies, in linear perturbation theory, depend only on the remnant’s mass and spin. These modes encode a unique spectral fingerprint of the final black hole, and current observations already hint at the presence of overtones.
To fully exploit these signals, we must develop a framework for quasinormal mode (QNM) interactions. The ringdown follows a highly nonlinear merger phase, and although numerical simulations suggest that a linear superposition of modes models the signal well, the connection to a fully nonlinear description remains unclear. A key difficulty is that Kerr QNMs do not form a complete orthogonal basis. Moreover, their spatial wavefunctions diverge at both the bifurcation sphere and spatial infinity, complicating the construction of canonical inner products on standard Cauchy hypersurfaces. Thus, it remains unclear how to project onto QNMs to study nonlinear mode mixing. In this talk, I will present bilinear forms that serve as inner-product analogues for Weyl scalars, constructed from conserved currents and symmetry operators. I will discuss their key properties on hyperboloidal slices, using the Schwarzschild spacetime as a model example. This work is in collaboration with Rodrigo Panosso Macedo, Christiana Pantelidou, and Laura Sberna.