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arXiv · 2608.06383

Reliable Weyl Diagnostics for an Inhomogeneous Universe in Numerical Relativity

Hassan Ugail
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Abstract

The electric and magnetic parts of the Weyl tensor provide a geometric diagnostic for describing the local gravitational structure of an inhomogeneous universe, and they allow us to distinguish tidal, gravitomagnetic, radiative, and silent regimes. However, when these diagnostics are computed from numerical relativity data, their interpretation depends on how well the data satisfy the Einstein constraint equations. A small constraint error can create a spurious magnetic signal, especially near a silent regime, and it may therefore be mistaken for genuine radiative structure. In this work, we treat the Hamiltonian and momentum constraint residuals as reliability gates for the Weyl diagnostics. Rather than imposing a fixed tolerance, we measure how a constraint error affects the corresponding Weyl classification, and we then calibrate the tolerance required to achieve a chosen accuracy. Our noise-induced synthetic tests show that the Hamiltonian residual determines the reliability of the electric Weyl diagnostic, whereas the momentum residual determines the reliability of the magnetic Weyl diagnostic. Furthermore, a real numerical relativity initial-data slice confirms that no universal tolerance is adequate. Thus, the calibration measures the slice-level sensitivity of the diagnostics rather than the truncation error of an evolution.

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Hassan Ugail. 2026-07-08. Reliable Weyl Diagnostics for an Inhomogeneous Universe in Numerical Relativity. https://arxiv.org/abs/2608.06383

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