Exploring black hole shadows in axisymmetric spacetimes with coordinate-independent methods and neural networks

TL;DR

This paper introduces coordinate-independent methods and neural networks to analyze black hole shadows across various spacetimes, enabling improved parameter estimation and tests of general relativity with observational data.

Contribution

It develops a coordinate-independent formalism combined with machine learning to characterize black hole shadows and constrain parameters from observational data.

Findings

Fourier expansion improves coordinate independence in shadow analysis

Neural networks accurately estimate black hole parameters from synthetic data

Constraints on black hole metrics derived from EHT and VLTI observations

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, $\gamma$, 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.