Investigating a New Approach to Quasinormal Modes: Physics-Informed Neural Networks

Abstract: Physics-informed neural networks (PINNs) hold the potential for supplementing the existing set of techniques for solving differential equations that emerge in the study of black hole quasinormal modes. The present research investigated them by studying black hole perturbation equations with known analytical solutions and thus could be framed as inverse problems in PINNs. Our main goal was to test the accuracy of PINNs in computing unknown quasinormal frequencies within the differential equations. The black hole perturbation scenarios that we considered included near extremal Schwarzschild-de Sitter and Reissner-Nordstr\"{o}m-de Sitter black holes, and a toy problem resembling them. For these cases, it was shown that PINNs could compute the QNFs with up to 4 digit decimal accuracy for the lowest multipole number, $l$, and lowest mode number, $n$.