Relativistic Angular-Speed Envelope ↔ PFT Coherence

Building on Nazat (2025), we adopt a universal angular-speed ceiling as a physical envelope for Allen Orbital Lattice (AOL) dynamics. In flat spacetime, ωmax=c/r. In curved spacetime (exterior Schwarzschild): ωmax,out= (c/r) · sqrt(1 - rs/r). For approximate interiors: ωmax,in= (c/r) · sqrt(1 - rs r² / R³). A Planck ceiling ωPlanck=c/ℓp ≈ 1.854×1043 rad/s caps classical rotation.

PFT Coherence Envelope. We enforce Equilibrion coherence by requiring: ωpattern(r) ≤ min{ ωmax(r), ωPlanck }. This guarantees AOL modes remain relativistically admissible and identifies curvature-induced suppression near compact objects.

Earth Weak-Field Consistency

Radius r (m)Regionωmax (rad/s)Remark
1Deep interior≈ 2.999 × 10⁸Near-flat limit
10³Inner crust≈ 2.997 × 10⁵Minor curvature
10⁶Mantle layer≈ 3.00 × 10²Weak curvature
R⊕Surface match≈ 4.71 × 10¹Joins exterior field

Exterior Corrections (Earth)

Radius r (m)Correctionωmax (rad/s)Δ%
R⊕1 − 6.95 × 10⁻¹⁰4.71 × 10¹−6.95 × 10⁻⁸%
1.496 × 10¹¹1 − 1.97 × 10⁻¹⁴2.0 × 10⁻³−1.97 × 10⁻¹²%

Strong Curvature: Schwarzschild Black Hole (M = M☉)

rωmax (rad/s)
rs0
1.5 rs3.9 × 10⁴
3 rs2.7 × 10⁴
10 rs9.6 × 10³
100 rs1.011 × 10³
1000 rs1.01 × 10²
10⁶ rs1.01 × 10⁻¹
Relativistic ωmax envelope across regimes (flat spacetime, Earth weak field, black hole curvature, and Planck ceiling). AOL coherence points (Pattern Field Theory) shown below the envelope.
Envelope: flat (red), Earth’s weak curvature (blue), Schwarzschild branch (black), and Planck ceiling (grey). All Allen Orbital Lattice (AOL) coherence modes in Pattern Field Theory remain below this physical limit.

Reference: Md. Shaikhul Hadis Nazat (2025), Universal Maximum Angular Speed for Objects in Flat and Curved Spacetime , Zenodo. DOI/Record: 17312907.

How to Cite This Article

APA

Allen, J. J. S. (2025). Relativistic Angular-Speed Envelope ↔ PFT Coherence. Pattern Field Theory. https://www.patternfieldtheory.com/articles/relativistic-angular-speed-envelope/

MLA

Allen, James Johan Sebastian. "Relativistic Angular-Speed Envelope ↔ PFT Coherence." Pattern Field Theory, 2025, https://www.patternfieldtheory.com/articles/relativistic-angular-speed-envelope/.

Chicago

Allen, James Johan Sebastian. "Relativistic Angular-Speed Envelope ↔ PFT Coherence." Pattern Field Theory. November 30, 2025. https://www.patternfieldtheory.com/articles/relativistic-angular-speed-envelope/.

BibTeX

@article{allen2025pft,
  author  = {James Johan Sebastian Allen},
  title   = {Relativistic Angular-Speed Envelope ↔ PFT Coherence},
  journal = {Pattern Field Theory},
  year    = {2025},
  url     = {https://www.patternfieldtheory.com/articles/relativistic-angular-speed-envelope/}
}