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) ≈ − 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, days, 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, Hz, GWF binary format, zlib extraction) yields fQNM = ± Hz consistent with GR for Mfinal ≈ 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 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.
