LIGO QNM Analysis¶

Compute quasi-normal mode frequency corrections for LIGO/Virgo gravitational wave events using the Choptyuk formula.

Theory¶

The Choptyuk correction modifies quasi-normal mode frequencies as:

\[ \omega^{\mathrm{corr}} = \omega \cdot \left(1 - \frac{1}{1200\pi^2}\right) \approx 0.999916 \cdot \omega \]

This produces a frequency shift of approximately \(\Delta f / f \approx 8.4 \times 10^{-5}\).

Quick Analysis¶

Use the LIGO analysis preset:

python run.py --preset ligo_analysis --non-interactive

Programmatic Usage¶

from src.core.qnm import QNMPredictor

predictor = QNMPredictor()
results = predictor.predict_all_events()

for event, data in results.items():
    print(f"{event}:")
    print(f"  f_QNM  = {data.f_qnm:.3f} Hz")
    print(f"  f_corr = {data.f_corrected:.3f} Hz")
    print(f"  Δf     = {data.delta_f:.4f} Hz")

Results¶

Event	\(f_{\mathrm{QNM}}\) (Hz)	\(f^{\mathrm{corr}}\) (Hz)	\(\Delta f\) (Hz)
GW150914	251.000	250.979	−0.0210
GW170104	293.000	292.975	−0.0246
GW170814	319.000	318.973	−0.0268
GW190521	110.000	109.991	−0.0092

Enhanced QNM (v2.0)¶

The v2.0 enhanced predictor includes:

Einstein GR corrections via Tyukovsky equations
K3 surface constraints (b₂ = 22)
Conformal invariance checks in 4D

from src.core.enhanced_verification import EnhancedQNMPredictor

enhanced = EnhancedQNMPredictor()
results = enhanced.predict_with_corrections(
    event="GW150914",
    include_einstein_gr=True,
    include_k3_constraints=True,
)

Physical Interpretation¶

The correction \(\delta_C^5 / 22 \approx 1/1200\) arises from the second-order spinor braking mechanism on the Klein quartic. This is a purely geometric effect — it depends only on the automorphism group PSL(2,7) and the genus-3 topology, not on the specific gravitational wave parameters.

The correction is small (\(\sim 10^{-4}\)) but potentially detectable with next-generation gravitational wave observatories (Einstein Telescope, Cosmic Explorer).