Constraints on a Saturating, Non‑Newtonian Substrate Model from GW150914 and GW190521
Abstract
We test predictions of the Finite-Response Coupled Field Dynamics (FRCFD) model—a saturable, non‑Newtonian substrate that replaces singularities with regime changes—using gravitational wave data from GW150914 and GW190521. Specific predictions examined include a fixed doublet near 200.2 Hz, amplitude modulation at the orbital frequency, two independent frequency tracks in the inspiral, spectral broadening, and a frequency “hook” (exponential recovery) in the ringdown. All predictions yield null results or inconsistent cross‑detector signals. We place upper limits on the model’s viscosity parameter η ≲ 2.5 (95% CL) from GW150914. For GW190521, we find no robust, detector‑consistent evidence for a frequency hook. The FRCFD framework remains mathematically coherent but is not yet supported by empirical evidence.
1. Introduction
General Relativity (GR) predicts singularities where curvature diverges and the theory ceases to describe physical reality. The FRCFD model replaces such divergences with saturation plateaus, a non‑Newtonian viscosity, and a threshold‑activated regulator (the “snap”). The model predicts a natural resonance (200.2 Hz) of the substrate, and specific observational signatures: a doublet, orbital beat, two‑ridge structure, spectral broadening, and a frequency “hook” in the ringdown.
This paper tests these predictions using REAL LIGO data from GW150914 and GW190521./p>
Constraints on a Saturating, Non‑Newtonian Substrate Model from GW150914 and GW190521
3. Methods
3.1 Data
We used REAL LIGO open data for GW150914 (GPS 1126259462.423) and GW190521 (GPS 1242442967.4). For each event, we extracted the ringdown segment (0–0.2 s after merger) and applied a bandpass filter (50–150 Hz or narrower variants). Analyses were performed on H1 and L1 data separately.
3.2 Prediction Tests
- Doublet & orbital beat: ESPRIT spectral estimation and envelope power spectrum.
- Two‑ridge detection: Spectrogram peak tracking with persistence filtering.
- Spectral broadening: Gaussian width of power spectrum vs. time.
- Frequency hook: Exponential recovery fit to instantaneous frequency using Hilbert transform with bounded optimization and bootstrap uncertainty.
3.3 Robustness Checks
We varied bandpass (65–115 Hz, 70–130 Hz), fit windows (5–60 ms, 5–100 ms), and used off‑event noise controls. Fits hitting parameter bounds were treated as upper limits.
4. Results
4.1 GW150914
- No doublet, no orbital beat, no persistent second ridge, no spectral broadening.
- Frequency hook fit did not converge to a physical τ.
Result: Upper limit on viscosity parameter η ≲ 2.5 (95% CL).
4.2 GW190521
- H1: τ = 1.0 ms (lower bound), η ≈ 0.05 (not robust).
- L1: τ = 30 ms (upper bound), η ≤ 1.5.
- Cross‑detector inconsistency prevents physical interpretation.
- Earlier candidate (τ ≈ 7.2 ms) did not survive stricter controls.
5. Discussion
The null results for GW150914 rule out several FRCFD sub‑hypotheses (doublet, beat, two ridges). The upper limit η ≲ 2.5 constrains nonlinear damping at the ∼60 M⊙ scale.
For GW190521, the lack of a consistent, cross‑detector hook indicates that the data do not provide a reliable measurement of η. The earlier candidate signature was likely a fitting artifact or noise structure.
The FRCFD framework remains mathematically viable but lacks empirical confirmation. Future observations (e.g., O4 catalog, LISA) may improve sensitivity.
6. Conclusion
We tested the FRCFD substrate model against two binary black hole mergers. No robust evidence for predicted signatures is found. The viscosity parameter is constrained to η ≲ 2.5. The model is not falsified but is not supported by current data.
7. Data and Code Availability
All code used in this analysis is available in a public repository (link to be added). Data are obtained from the LIGO Open Science Center.
