Michele Lenzi (ULB, Belgium)

Spectral features of perturbed black holes from hidden symmetries

Perturbation theory of vacuum, spherically symmetric spacetimes is a long-established but crucial tool for understanding black-hole (BH) dynamics, including scattering phenomena and the ringdown of binary BHs. While perturbation equations are known to decouple into gauge-invariant master functions satisfying 1+1 wave equations, recent works have shown that Einstein’s equations admit an infinite set of them, revealing new hidden symmetries in the dynamics of perturbed, non-rotating BHs: Darboux covariance and the infinite hierarchy of Korteweg-de Vries (KdV) deformations of the master equation. These results establish a novel connection with integrable systems, linking physical properties of perturbed BHs, such as greybody factors, to the conserved quantities of the KdV hierarchy. We will discuss these findings and outline possible future directions emerging from them.