EHT Shadow Correction

τ-Formula

f_τ = 1 + ι_τ²/4 = 1.02912 (+2.91% universal)

Derivation

• Shadow diameter: $θ_τ = 40.85\,μas$.
• EHT observation: $42 ± 3\,μas$.
• Deviation: $0.4σ$.
• QNM ratio: $ι_τ^-1 ≈ 2.930$.
• Modulation periods: $4.66$ d (outer $S^1$), $1.59$ d (inner $S^1$).

The shadow prediction lies comfortably within the EHT error bar. The $T^2$ correction brings $τ$ $1.15\,μas$ closer to the central value than pure GR.

Source

This prediction is derived in the Physics Ledger (Chapter 64 — black-hole-topology), Books IV–V of Panta Rhei.