Teukolsky by Design: A Hybrid Spectral-PINN solver for Kerr Quasinormal Modes
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| Format: | Preprint |
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2025
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| author | Pombo, Alexandre M. Pizzuti, Lorenzo |
| author_facet | Pombo, Alexandre M. Pizzuti, Lorenzo |
| contents | We introduce SpectralPINN, a hybrid pseudo-spectral/physics-informed neural network (PINN) solver for Kerr quasinormal modes that targets the Teukolsky equation in both the separated (radial/angular) and joint two-dimensional formulations. The solver replaces standard neural activation functions with Chebyshev polynomials of the first kind and supports both soft -- via loss penalties -- and hard -- enforced by analytic masks -- implementations of Leaver's normalization. Benchmarking against Leaver's continued-fraction method shows cumulative (real+imaginary part) relative frequency errors of $\sim 0.001\%$ for the separated formulation with hard normalization, $\sim 0.1\%$ for both the soft separated and soft joint formulations, and $\sim 0.01\%$ for the hard joint case. Exploiting our ability to solve the joint equation, we add a small quadrupolar perturbation to the Teukolsky operator, effectively rendering the problem non-separable. The resulting perturbed quasinormal modes are compared against the expected precision of the Einstein Telescope, allowing us to constrain the magnitude of the perturbation. These proof-of-concept results demonstrate that hybrid spectral-PINN solvers can provide a flexible pathway to quasinormal spectra in settings where separability, asymptotics, or field content become more intricate and high accuracy is required. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_15796 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Teukolsky by Design: A Hybrid Spectral-PINN solver for Kerr Quasinormal Modes Pombo, Alexandre M. Pizzuti, Lorenzo General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena We introduce SpectralPINN, a hybrid pseudo-spectral/physics-informed neural network (PINN) solver for Kerr quasinormal modes that targets the Teukolsky equation in both the separated (radial/angular) and joint two-dimensional formulations. The solver replaces standard neural activation functions with Chebyshev polynomials of the first kind and supports both soft -- via loss penalties -- and hard -- enforced by analytic masks -- implementations of Leaver's normalization. Benchmarking against Leaver's continued-fraction method shows cumulative (real+imaginary part) relative frequency errors of $\sim 0.001\%$ for the separated formulation with hard normalization, $\sim 0.1\%$ for both the soft separated and soft joint formulations, and $\sim 0.01\%$ for the hard joint case. Exploiting our ability to solve the joint equation, we add a small quadrupolar perturbation to the Teukolsky operator, effectively rendering the problem non-separable. The resulting perturbed quasinormal modes are compared against the expected precision of the Einstein Telescope, allowing us to constrain the magnitude of the perturbation. These proof-of-concept results demonstrate that hybrid spectral-PINN solvers can provide a flexible pathway to quasinormal spectra in settings where separability, asymptotics, or field content become more intricate and high accuracy is required. |
| title | Teukolsky by Design: A Hybrid Spectral-PINN solver for Kerr Quasinormal Modes |
| topic | General Relativity and Quantum Cosmology High Energy Astrophysical Phenomena |
| url | https://arxiv.org/abs/2511.15796 |