On gravity at large (galactic) scales

The baryonic Tully–Fisher relation logM_bar=c+blogV_flat 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. M_bar 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 (V_flat≈45...280km/s). Slope b=2 appears in modeling [2;App.G] (except for dwarfs); this indicates F~M_bar/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 M_R inside R: F(R)/m=GM_R/(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).