שמור ב:
| מחבר ראשי: | |
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| פורמט: | Recurso digital |
| שפה: | |
| יצא לאור: |
Zenodo
2026
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| נושאים: | |
| גישה מקוונת: | https://doi.org/10.5281/zenodo.19369902 |
| תגים: |
הוספת תג
אין תגיות, היה/י הראשונ/ה לתייג את הרשומה!
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תוכן הענינים:
- <p>We apply the Lagrangian–Jacobian diagnostic framework from the Thales partition manifold to five binary black hole merger events: GW150914 (GWTC-1) and four events from the GWTC-3 catalog (GW191215, GW200220, GW200308, GW200322). The rapidity-convention Jacobian J = −sinh(ξ) = −χ/√(1−χ²) satisfies four structural identities to machine precision (< 10⁻¹⁴) on both the intrinsic mass partition (from Bayesian posterior samples) and the extrinsic detector partition (from LIGO H1/L1 strain data), confirming that the Thales constraint surface is a valid diagnostic manifold for gravitational wave data.</p> <p>Three principal results emerge. First, the mass shell identity R − J² = 1, where R = 1/(4h²) is the altitude parameter and h = √(ab) the Thales altitude of the mass partition a = m₁/M, holds exactly on all five events, establishing the Lorentz hyperboloid as a verified geometric structure in binary black hole parameter space. Second, the Thales deficit δ = 1 − 2h anti-correlates with fractional radiated energy at Pearson r = −0.974 (p = 0.005): more asymmetric mass partitions radiate less efficiently, with the symmetric mass ratio η = h² providing the geometric coupling efficiency. The stability ratio r_in/h matches √2 − 1 to within 0.04% for the near-equal-mass GW150914, with systematic deviation proportional to the manifold Lorentz factor γ = 1/(2h) as predicted. Third, the time-resolved GW150914 detector partition reveals the merger as a rebalancing event: the detector asymmetry χ collapses from 0.77 to 0.08, the coupling altitude h rises from 0.32 to 0.50 (near-equipartition), the rapidity momentum |J| falls from 1.26 to 0.08, and the altitude parameter R falls from 2.68 to 1.01, as the gravitational wave signal coherently drives the two-channel detector partition toward balance. The merger corresponds to a rapidity collapse toward the rest frame of the Lorentz hyperboloid — a geometric rebalancing rather than a Hamiltonian takeover.</p> <p>The compound channel diagnostic (manifold telescope A = γ_E/γ_M) reveals that the angular separation between the mass and spin partition faces narrows from 9.4° for near-equal-mass systems to 3.0° for asymmetric systems, consistent with spin being determined by orbital angular momentum rather than by the reconciliation of misaligned constraint circles. All results are diagnostic applications of the constraint a + b = 1 and the geometric mean h = √(ab); no modification of gravitational dynamics is proposed.</p>