https://doi.org/10.1140/epjc/s10052-025-14945-w
Regular Article - Theoretical Physics
Exploring black hole shadows in axisymmetric spacetimes with coordinate-independent methods and neural networks
1
Center for Astronomy and Astrophysics, Center for Field Theory and Particle Physics, and Department of Physics, Fudan University, 200438, Shanghai, China
2
Institute for Advanced Studies, New Uzbekistan University, Movarounnahr str. 1, 100007, Tashkent, Uzbekistan
3
School of Physics, Harbin Institute of Technology, 150001, Harbin, People’s Republic of China
4
Institute of Theoretical Physics, National University of Uzbekistan, 100174, Tashkent, Uzbekistan
5
School of Natural Sciences and Humanities, New Uzbekistan University, 100007, Tashkent, Uzbekistan
a
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Received:
13
August
2025
Accepted:
12
October
2025
Published online:
23
October
2025
Abstract
The study of black hole shadows provides a powerful tool for testing the predictions of general relativity and exploring deviations from the standard Kerr metric in the strong gravitational field regime. Here, we investigate the shadow properties of axisymmetric gravitational compact objects using a coordinate-independent formalism. We analyze black hole shadows in various spacetime geometries, including the Kerr, Taub-NUT, 
, and Kaluza-Klein metrics, to identify distinctive features that can be used to constrain black hole parameters. To achieve a more robust characterization, we employ both Legendre and Fourier expansions, demonstrating that the Fourier approach may offer better coordinate independence and facilitate cross-model comparisons. Finally, we develop a machine learning framework based on neural networks trained on synthetic shadow data, enabling precise parameter estimation from observational results. Using data from observational astronomical facilities such as the Event Horizon Telescope (EHT), Keck, and the Very Large Telescope Interferometer (VLTI), we provide constraints on black hole parameters derived from shadow observations. Our findings highlight the potential of coordinate-independent techniques and machine learning for advancing black hole astrophysics and testing fundamental physics beyond general relativity.
© The Author(s) 2025
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Funded by SCOAP3.
