Registry · Theorem
V.T169
tau-effective
formalized
V.T169 — GW Echo Times t± = 4GM·ι_τ^{±1}/c³
GW echoes from the T² horizon arise at t_outer=4GM·ι_τ⁻¹/c³ (outer S¹ round trip) and t_inner=4GM·ι_τ/c³ (inner S¹). Echo separation Δt=4GM(ι_τ⁻¹-ι_τ)/c³=4GM(1-ι_τ²)/(c³·ι_τ). Lab results: M=30 M_☉: t_outer=1.7321 ms, t_inner=0.2018 ms, Δt=1.5303 ms. For GW150914 (M≈62 M_☉): Δt=3.1626 ms. Table: M=10: Δt=0.5101 ms; M=30: Δt=1.5303 ms; M=62: Δt=3.1626 ms; M=150: Δt=7.6515 ms.
Book V
Part 6
Ch. 51