The Jacobian Diagnostic on LIGO Binary Black Hole Data: Structural Identities, Rebalancing Dynamics, and the Deficit–Radiative Efficiency Correlation
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2026
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| author | De Jesus, Elias |
| author_facet | De Jesus, Elias |
| contents | <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> |
| format | Recurso digital |
| id | zenodo_https___doi_org_10_5281_zenodo_19369902 |
| institution | Zenodo |
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| publishDate | 2026 |
| publisher | Zenodo |
| record_format | zenodo |
| spellingShingle | The Jacobian Diagnostic on LIGO Binary Black Hole Data: Structural Identities, Rebalancing Dynamics, and the Deficit–Radiative Efficiency Correlation De Jesus, Elias binary black hole, Thales partition, Jacobian, rapidity, Lorentz hyperboloid, mass shell identity, gravitational waves, GWTC-3, GW150914, Thales altitude, symmetric mass ratio, coupling efficiency, deficit, radiative efficiency, rebalancing, equipartition, stability ratio, Poincaré metric, constraint geometry, partition manifold <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> |
| title | The Jacobian Diagnostic on LIGO Binary Black Hole Data: Structural Identities, Rebalancing Dynamics, and the Deficit–Radiative Efficiency Correlation |
| topic | binary black hole, Thales partition, Jacobian, rapidity, Lorentz hyperboloid, mass shell identity, gravitational waves, GWTC-3, GW150914, Thales altitude, symmetric mass ratio, coupling efficiency, deficit, radiative efficiency, rebalancing, equipartition, stability ratio, Poincaré metric, constraint geometry, partition manifold |
| url | https://doi.org/10.5281/zenodo.19369902 |