PUH Theorem 387 — Gravitational Waves Turn a Planck Core Toward Co-Rotation: Faster Waves Spin It Up, Slower Waves Spin It Down; the Core Grows Only by Amalgamation, and the Rest Leaves at the Poles

Abstract

Photonic Universe Hypothesis (PUH) — Theorem paper. THE QUESTION. The archive holds that the Planck Shell absorbs gravitational waves and returns nothing (T307, T308), which is why no echoes are seen; it followed the waves' energy, not their angular momentum. The author's point: a Planck core grows only by amalgamation; it unfolds spacetime and matter into high-energy photons, and its drain is already at its maximum, so mass piles up around it (T210); a gravitational wave striking it changes its spin — up if the wave goes faster, down if slower — which changes its magnetic field and, in turn, slightly changes the energy released from its poles. RESULT 387.1 — A CORE GROWS ONLY BY AMALGAMATION. The archive holds two readings: growth by what a core takes in (T206(a), T288, T287's Channel B, T307's gain) and growth only by merging (the Stellar Planck Core Lead Note, section 2.4; the author). In the author's, what reaches the Shell is unfolded into high-energy photons and passed out at the poles (T210, T368); the drain is capped (one Planck layer per Planck time) and far slower than infall (T330: about 350 kW for a solar-mass core), so mass piles up around the core and what cannot yet pass waits at the Shell (T308). The cap is on lattice rate, not on the energy each unfolded site carries (up to 9 E_P, T166). T287's runaway to the final Planck star and T347's concentration of cores stand on amalgamation alone. RESULT 387.2 — A WAVE'S ANGULAR MOMENTUM MUST GO INTO THE SPIN. A wave pattern carries J/E = m/omega exactly (outgoing modes: 1.000000, 2.000000, 8.000000, 1.500000 against m/omega). The core cannot store it by growing; polar photons can carry at most 3.341e-18 of it (helicity); the spinning field carries it off only over 1.707e25 years or more (10 solar masses, chi = 0.7). The spin keeps it. RESULT 387.3 — FASTER WAVES SPIN IT UP, SLOWER WAVES SPIN IT DOWN. In the light bulb (T357) the Shell turns at Omega_s = 0.32334 chi c^3/GM (R = 2.15385 GM/c^2, X = 14). Of an absorbed wave's energy, rotation keeps Omega_s dJ and the rest, dJ (omega/m - Omega_s), leaves through the poles. The poles only send energy out, so the spin moves toward co-rotation with the wave's pattern: up for faster waves, down for slower ones. At chi = 0.7, rotation keeps 0.9054 of a wave at GM omega/c^3 = 0.5. A polar cap that turns with the Shell multiplies the polar share by 1/(1 - (v_cap/c)^2) (1.00722 for a 10-degree cap at chi = 0.7, 1.13487 for a 30-degree cap at chi = 0.99) and leaves the direction unchanged. RESULT 387.4 — HOW MUCH. d chi = eps (m/x)(1 - 2 k chi^2), k = 0.32334, x = GM omega/c^3: 4 per unit absorbed Mc^2 at x = 0.5 for a non-spinning core. Waves settle the spin at chi_eq = (GM(omega/m)/c^3)/k (0.7732 at x = 0.5); a companion's tide turns the core toward co-rotation with the orbit (chi_eq = 0.1546 at G M Omega_orb/c^3 = 0.05). The cosmic background (NANOGrav 15 yr) could deliver at most 3.3062e-24 of a 4e6-solar-mass core's Mc^2 in 13.8 Gyr, with no net spin. RESULT 387.5 — THE FIELD FOLLOWS THE SPIN, AND THE POLES RELEASE A LITTLE MORE. The Shell-Dynamo field is proportional to the spin rate. T370's field-driven polar power, the magnetic spin-down power B^2 R^6 Omega^4/(6c^3), then grows as chi^6 and is the same for every core at the same spin (7.7943e7 W at chi = 0.7 with electron carriers, 2.6278e14 W with proton carriers). Absorbing 1e-4 of its Mc^2 from faster waves raises it by 0.7534 per cent (chi = 0.3, x = 0.5) to 5.9612 per cent (chi = 0.1, x = 0.2): the author's slight increase. Slower waves lower it. NOT CLAIMED: how much a Shell absorbs; the absolute size of the extra polar output; the carrier ratio; a relativistic moment of inertia for the Shell; anything in Einstein's equations. KILL-CONDITIONS: a Planck core shown to grow other than by amalgamation; polar output that takes energy in or carries axial angular momentum comparable to m/omega per unit energy; post-merger echoes at T311's delay. OPEN: how much a Shell absorbs; the carrier ratio; how the final core comes to hold the folded lattice (T242); T244's gating and universal spin; where Sgr A*'s accreted energy goes, against its observed limits (Broderick, Loeb and Narayan 2009).