What question did this study set out to answer?

This research aims to extend the prediction of gravitational wave echoes from Schwarzschild to Kerr black holes, focusing on measuring spin.

March 26, 2026Open Access

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

Key Points

This research aims to extend the prediction of gravitational wave echoes from Schwarzschild to Kerr black holes, focusing on measuring spin.
Developed a two-dimensional surface model Δf(M, a*) for black hole mass and spin.
Tabulated echo frequency spacing Δf for varying parameters M and a*.
Utilized measurements from the Einstein Telescope to determine spin independently of ringdown analysis.
Found that echo frequency spacing Δf decreases with spin, specifically Δf ≃ 0.25 × Δf_Schwarzschild for a*=0.99.
Established that the model uniquely determines spin from M and Δf, enhancing black hole characterization.
Demonstrated the Δf(M, a*) surface as a unique prediction with no existing general relativity counterpart.

Abstract

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 × ΔfSchwarzschild. 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.

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Marc López Sánchez

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

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