DENSITY vs COLLAPSE TIME
GR — diverges to ∞ (singularity)
BFUT — saturates at ρ_max_finite
BFUT ρ/ρs
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GR ρ/ρs
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STABILISING MECHANISMS — toggle to see what each does
T4 Restoring Pressure — substrate pushes back against compression
T4: Vacuum Stabilisation Pressure
P_restore = (ρs/4)(ρ − ρs)
The Spaticle field has an equilibrium density ρs. Any compression above this costs energy proportional to the square of the excess. The substrate literally pushes back, like compressing a very stiff spring. Derived directly from the Spaticle field Lagrangian.
C|ψ|⁶ Higher-Order Repulsion — extreme compression hits a hard wall
C|ψ|⁶: Superlinear Hard Repulsion
P_repulsion = 3C ρ²
At very high densities the repulsion grows faster than the compression force. No matter how strong the inward collapse, this term eventually wins. It sets the hard upper bound on density — rho_max_finite. The substrate cannot be compressed beyond this point.
J_entrain Redistribution — rotation moves energy outward continuously
J_entrain: Outward Redistribution Flux
ρ_eff(r) = ρ(r) − ∇·J_entrain
A rotating collapsing object entrains the Spaticle substrate into rotation. This centrifugally drives organised deformation outward from the core into the surrounding shell. Energy is continuously removed from the core, relieving compression. The faster the rotation, the stronger this effect.
COLLAPSE STAGE
1. Normal star — moderate substrate deformation
2. Neutron-star regime — strong compression begins
3. Compression core forms — restoring mechanisms activate
4. Saturation — density approaches ρ_max_finite
5. Stable compact structure — GR would still diverge here
REPLACEMENT OBJECT — 4 REGIONS
Compressed Core
ρ_max_finite. Radius ~2 km. Circulates at maximum coherent rate. No singularity — finite density, finite volume.
Redistribution Shell
J_entrain active. Continuously carries deformation outward from core into surrounding field.
Coherence Boundary
Analogue of event horizon — but NOT a one-way causal surface. Boundary between organised compression and normal gravitational field.
Outer Entrainment
Extends to R_d = (3M/8πρs)^(1/3). Contributes to flat rotation curves at galactic scale.
▶ KEY VALIDATED PREDICTION
Carrier relaxation time τ_c = 4.6 ms predicted from ρs alone. GW170817 neutron star merger measured τ ≈ 6.8 ms — within the BFUT predicted window of 1–15 ms (Paper 18).