Relativity and Cosmology

Spiral Galaxies: Explanation for Their Morphological Structure, Logarithmic Geometry, and Velocity Curve Flattening in the Pivot Universe Mode

Authors: Arieh Sher

We investigate the kinematic and morphological properties of disk and spiral galaxies withinthe Pivot Universe (PU) theoretical framework. In this model, the persistent flattening of galacticrotation curves is attributed to an asymptotic background spacetime frame-dragging field (Ω0)induced by the cosmic Kerr pivot, eliminating the need for cold dark matter (CDM) halos. Bycoupling the local baryonic mass distribution to this background metric acceleration field (a0), theBaryonic Tully-Fisher Relation (V 4flat ∝ Ga0Mb) is derived directly from first principles.Furthermore, we examine galactic morphology resulting from continuous ballistic mass ejectionfrom rotating antipodal nozzles anchored to central supermassive black holes (SMBHs). Whileinitial formulations assumed Archimedean spirals (r ≈ bθ), we demonstrate that transitioningto a logarithmic spiral geometry (r = aebθ) is physically required to resolve the outer windingproblem and preserve self-similarity. We show that a logarithmic geometry naturally couples withan asymptotically flat rotation curve (vϕ = const), as the required angular dragging frequencyscales as ω(r) ∝ 1/r.Analytical rotation curves and structural models are derived and benchmarked against empiricalobservations for the Milky Way, the grand-design spiral NGC 5457 (M101), the barred lenticulargalaxy NGC 2787, and the Whirlpool Galaxy (M51). Finally, we introduce a non-linear tidalperturbation correction term, δr(θ), demonstrating how external gravitational interactions withsatellite dwarf galaxies (such as NGC 5474) break intrinsic m = 2 antipodal symmetry to producethe observed lopsidedness and arm elongation in M101.Keywords: Galaxies: kinematics and dynamics — Galaxies: spiral — Galaxies: structure — Cosmology: theory — Metric frame-dragging — Tully-Fisher relatio

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[v1] 2026-09-14 14:25:49

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