We determine and characterize the full space of master equations describing the dynamics of perturbed Schwarzschild black holes and show that all of them are connected via Darboux transformations. This reveals the presence of a hidden symmetry, Darboux covariance, which preserves the spectrum of quasinormal modes and the continuous spectrum associated with black hole scattering processes. This picture is shown to share a deep connection with the Korteweg-de Vries equation and inverse scattering methods which leads to an infinite hierarchy of conserved quantities.

• Received 2 September 2021
• Accepted 10 December 2021

DOI:https://doi.org/10.1103/PhysRevD.104.124068