Solving the Teukolsky equation with physics-informed neural networks

We use physics-informed neural networks (PINNs) to compute the first quasinormal modes of the Kerr geometry via the Teukolsky equation. This technique allows us to extract the complex frequencies and separation constants of the equation without the need for sophisticated numerical techniques, and with an almost immediate implementation under the PyTorch framework. We are able to compute the oscillation frequencies and damping times for arbitrary black hole spins and masses, with accuracy typically below the percentual level as compared to the accepted values in the literature. We find that PINN-computed quasinormal modes are indistinguishable from those obtained through existing methods at signal-to-noise ratios (SNRs) larger than 100, making the former reliable for gravitational-wave data analysis in the mid term, before the arrival of third-generation detectors like LISA or the Einstein Telescope, where SNRs of Oo1000 thorn might be achieved.

Automated summary

We use physics-informed neural networks (PINNs) to compute the first quasinormal modes of the Kerr geometry via the Teukolsky equation, providing accurate oscillation frequencies and damping times for black holes. The PINN-computed quasinormal modes are indistinguishable from existing methods at high signal-to-noise ratios (SNRs), making them reliable for gravitational-wave data analysis in the mid term. This technique may continue to be useful until the arrival of third-generation detectors with higher SNRs.