A Hybrid Pseudo-spectral–PINN Approach to Black Hole Quasinormal Modes

Gravitational-wave detections by the LIGO-Virgo-KAGRA network have turned compact-object mergers into precision probes of strong gravity. The post-merger ringdown is particularly incisive: it is governed by quasinormal modes (QNMs), the damped oscillations that encode the remnant's structure and provide a fingerprint of the final object. While current detectors constrain the dominant mode, next-generation observatories will resolve multiple modes with high precision, placing stringent demands on the accuracy of theoretical predictions. Computing QNMs for rotating black holes is, however, a non-trivial task, as it requires solving highly coupled, complex-valued perturbation equations where standard methods struggle. In this talk, I present SpectralPINN, a hybrid solver combining Pseudo-spectral methods with Physics-Informed Neural Networks, validated at 10⁻⁵ relative accuracy. I will present results for Kerr and Kerr-Newman black holes, demonstrating the method's robustness and accuracy across parameter space, and discuss its potential for extension to more exotic compact objects relevant to next-generation detector science.