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On gravity at large (galactic) scales
1  Laboratory # 9 (Synchrotron Radiation methods), Institute of Solid State Chemistry and Mechanochemistry of the Siberian Branch of the Russian Academy of Sciences (ISSCM SB RAS), Novosibirsk, 63000, Russia
Academic Editor: Lorenzo Iorio

Abstract:

The baryonic Tully–Fisher relation logMbar=c+blogVflat links the baryonic mass of spiral-galaxies with their asymptotic velocity. Flat rotation curves suggest extra-gravity at galactic scales, which is explained by dark matter. However, astrophysicists point to facts/data that contradict the DM-hypothesis (P.Kroupa). Instead, the MOND-model is advocated, which requires b=4. Mbar includes stars, atomic/molecular gas, and HI/HeI/H2; for dwarfs, HII-component is important (intergalactic radiation ionizes, as N.Gnedin notes). Сonducting calculations is hard and requires assumptions/modeling; in [1] slope b≈3 was obtained for spirals (Vflat≈45...280km/s). Slope b=2 appears in modeling [2;App.G] (except for dwarfs); this indicates F~Mbar/R gravity;.This is possible for one 5D-variant of Teleparallelism with 4th-order gravity and expanding brane-universe [3]: Newton's law transforms to F/m=GM/(LR) when R>L (L is brane's co-moving thickness along the extra-dimension). This model, called MOGA, unlike MOND, preserves the momentum/angular momentum and stability of three-body systems (Toxvaerd S. arXiv:2512.03823; MOdifiedGravityAttraction).

For thin (SO2-symmetry; 1/R-model) disks, the force/acceleration in the disk-plane, at radius R, depends on the mass MR inside R: F(R)/m=GMR/(LR); on the axis (uniform discs, radius a; 'test-mass' m): F(Z)/m=GMZ/(La2) ln(1+a2/Z2). For balls/bulges, one finds (let GMm/L=1):
F(R)=3/(8a){a/R+R/a–0.5(a/R–R/a)2 ln[(R+a)/|R–a|]}=R/a2{1–(R/a)2/5–...–3(R/a)2n/[(2n–1)(2n+1)(2n+3)]–...}=1/
R{1–(a/R)2/5–...}.

Logarithmic potential growth stops when "underdensities" appear, and voids should be objects with negative masses. Our MW-galaxy resides in the KBC-void (among the largest—redshift z is small!) with a shift from its center. Defocussing caused by the KBC-void provides some extra-dipoles (redshift-dependent).

1. Ponomareva A.A. etal. MNRAS.474(2018)4366(hal-02117129f).
2. Valageas P., Schaeffer R. Astron.Astrophys.345(1999)329(arXiv:astro-ph/9812213).
3. Zhogin I.L. Space,Time&Fund.Inter.#2(2025)40(stfi.ru/journal/STFI_2025_02/STFI_2025_02_Zhogin.pdf).

Keywords: baryonic Tully-Fisher relation; Absolute Parallelism; 4th-order gravity in 5D AP

 
 
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