Black Holes as Topological Winding Structures: An Exploratory Framework with Observational Constraints from EHT and LIGO
Michel ALdon
Abstract
We present ATPEW (ALdon Theory of Primordial Energy Wave), an exploratory conceptual framework in which all physical objects are topological vortex configurations of a single complex scalar field Ψ = ÷exp(iθ), governed by the Lagrangian: ℒ = α(∂μÃ)² + βò(∂μθ)² − λÃ⁻² − μ²Ã² In this framework, a black hole is a spherically stratified structure — two concentric spheres of radii rcore and rph delimiting five functionally distinct zones — whose internal phase field carries a closed toroidal winding of number k. The hollow core of this structure, a wave vacuum where no stable frequency mode can form, lies beneath the Schwarzschild horizon when the winding number k exceeds the topological closure threshold kseuil = rs·√(2μ²/β). The event horizon is not a mathematical surface but a waveguide condition: modes with angular frequency ω < ωcut(r) = clocal(r)·k/r are guided inward rather than transmitted outward, exactly as electromagnetic modes below cutoff in a metallic waveguide. No singularity arises because the λÃ⁻² term enforces a finite minimum amplitude fmin = (λ/μ²)1/4 at the core boundary — the field exists at its minimum, but never vanishes. We show that the Schwarzschild metric is exactly recovered at zeroth order in β/μ² (Appendix A): when the winding coupling term is negligible, the amplitude equation reduces to a spherical Yukawa equation whose solution f(r) ≈ 1 − rs/(2r) reproduces gtt = −c²(1−rs/r) for Yukawa range ξ >> rs. The framework is confronted with two independent observational datasets. Analysis of 91,846 EHT visibility measurements of M87* (2018, 3 days, 4 frequency bands, 213–229 GHz, HOPS and CASA pipelines) yields a photon ring diameter of 41.1 μas, a +3.6% excess over the GR prediction of 39.7 μas, constraining β/(μ²·rs²) ≈ 0.056 (k=5). Analysis of raw LIGO GW150914 strain data (H1 detector, 4096 Hz, GWF binary format, zlib extraction) yields fQNM = 249 ± 7 Hz consistent with GR for Mfinal ≈ 68 M☉, with correction δf/f < 0.2%. Both results are consistent with the weak-coupling regime β̃/μ̃² << 1. The framework predicts a universal hierarchy of topological transitions spanning 28 orders of magnitude in scale, from quarks (k = 2π/3) to supermassive black holes (k ~ 10⁶⁶), with numerically computed threshold values k₁ = 1.71×10⁵⁷ (Chandrasekhar limit), k₂ = 2.4–3.6×10⁵⁷ (TOV limit), and k₃ > 3.6×10⁵⁷ (black hole formation). Three qualitatively distinct merger regimes are predicted depending on phase alignment. Hawking evaporation is reinterpreted as spontaneous quantum unraveling of the spiral tail, yielding TATPEW ∝ 1/M with the correct order of magnitude. Ten observational predictions distinguishable from GR are identified, testable by next-generation EHT, future LIGO catalogs, and next-generation gravitational wave detectors. Three explicit open mathematical problems are listed.