CCEGA Paper 22: Gravitational Wave Echoes from Kerr Black Holes — The Δf(M, a*) Surface as a Spin Measurement Tool

Extends the CCEGA gravitational wave echo prediction from Schwarzschild to Kerr black holes. The echo frequency spacing Δf decreases monotonically with spin: for a*=0.99, Δf ≃ 0.25 × Δf_Schwarzschild. The complete prediction is a two-dimensional surface Δf(M, a*), tabulated for M ∈ [5,50] Msun and a* ∈ [0, 0.99]. A measurement of Δf by the Einstein Telescope, combined with the chirp mass M, uniquely determines the remnant spin a* — providing a spin measurement independent of ringdown analysis. This transforms the CCEGA echo prediction from a binary detection into a quantitative measurement: CCEGA becomes a spin measurement tool. The Δf(M, a*) surface is a unique, zero-free-parameter prediction with no GR analogue.