Kerr quasinormal modes without separation of variables: a 2D hyperboloidal Teukolsky solver with physics-informed neural networks

Abstract

Separation of variables is what makes the Kerr quasinormal-mode problem tractable, and it is exactly what is lost for most beyond-Kerr black holes. We present a solver that never separates. The Teukolsky equation is posed on compactified hyperboloidal slices, where the eigenfunctions are regular from the horizon out to future null infinity, and we solve the resulting two-dimensional problem with a physics-informed neural network whose frequency is a trainable parameter optimized jointly with the field. Branches are built by spin continuation. For six modes, every computed frequency agrees with independent reference spectra to better than 0.5%, including the near-extremal, zero-damping regime. We discuss the accuracy trade-off against dedicated spectral Kerr solvers, and the extension to non-separable backgrounds and coupled systems.