Sensitivity of model visibilities to Kerr metric deformations from EHT data for M87*: the role of astrophysical systematics and emitter kinematics

CONTEXT. Observations by the Event Horizon Telescope (EHT) of the shadow of M87* have opened the possibility of testing spacetime geometry in the strong-field regime. A fundamental obstacle remains degeneracy: can a metric deformation be distinguished from uncertainties of the accretion-disk model? WHAT WE DO. We study how diagonal deformations of the inverse Kerr metric, g^μν → g^μν [1 + ε (M/r)²], manifest in interferometric visibilities. Three classes of deformations are considered: g^tt, g^rr, g^φφ. Model visibilities are compared with EHT data for M87* (Stokes I, 11 April 2017). The quantitative χ² analysis and renormalization are restricted to g^tt. The hybrid construction — Kerr kinematics of the emitter + deformed photon sector — is explicitly tested through the four-velocity norm N(ε, r, θ) = −g^def_μν u^μ u^ν. KEY RESULTS.• Metric signature. In |ε| ≤ 0.20 the deformed metric remains non-degenerate and Lorentzian: the eigenvalues of the (t, φ) block have opposite signs, g_rr > 0, g_θθ > 0, det g < 0.• Timelike four-velocity. N > 0 for |ε| ≤ 0.05 (confirmed numerically and structurally); for ε ≥ +0.10, N < 0 at the ISCO — the hybrid model becomes inconsistent.• Geodesicity. For ε ≠ 0 the radial residual |a^r| r² ~ 0.1–0.3 at the ISCO; renormalization of u^μ corrects the norm but does not make the orbits geodesic. The model is therefore normalized phenomenological, not self-consistent.• Renormalized analysis. In the working interval |ε| ≤ 0.05, the sign of Δχ² is preserved, |Δχ²| decreases by a factor 1.43–2.52, and D_corr ≤ 0.284% (convergence not verified).• Fit quality. All considered models give χ²/N ≈ 16–20 for visibilities and ≈ 21–40 for closure phases. In this situation, Δχ² cannot be interpreted as statistical significance. CONCLUSION. The magnitude of the formal preference between metric models depends on the source model and on the prescription for emitter kinematics. The procedure for constructing the hybrid model is itself capable of substantially changing the formal sensitivity to the deformation. Rigorous constraints on ε require self-consistent geodesic orbits, a full source model, and a correct covariance matrix.