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

TL;DR

This paper explores the use of physics-informed neural networks to accurately compute quasinormal frequencies of black hole perturbations, demonstrating high precision in complex scenarios.

Contribution

It introduces a novel application of PINNs to black hole quasinormal mode calculations and assesses their accuracy against known analytical solutions.

Findings

PINNs achieved up to 4-digit accuracy in computing QNFs.

Effective for near extremal Schwarzschild-de Sitter and Reissner-Nordström-de Sitter black holes.

Validated PINNs as a promising tool for solving inverse problems in black hole physics.

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, $n$.