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SUMMARY:Gravitational repulsion of spherical Voids (MOGA-model with large-
 scale force 1/$R$)
DTSTART;VALUE=DATE-TIME:20261027T162500Z
DTEND;VALUE=DATE-TIME:20261027T163000Z
DTSTAMP;VALUE=DATE-TIME:20261021T100007Z
UID:indico-contribution-6455@cern.ch
DESCRIPTION:Speakers: Ivan Zhogin (ISSCM SB RAS)\nFlat rotation curves of 
 galaxies suggest extra gravity at galactic scales\, which is usually expla
 ined by dark matter (DM). However\, astrophysicists \n([P. Kroupa et al][1
 ])\npoint to facts and data that contradict the DM hypothesis. Instead\, t
 he MOND model is advocated. The baryonic Tully–Fisher relation\n $\\log 
 M_ {\\rm bar} = c + b \\log V_{\\rm flat}$ links the baryonic mass of spir
 al galaxies with their asymptotic velocity. MOND requires $b = 4$. The $M_
 {\\rm bar}$ includes stars\, atomic and molecular gas (i.e. HI/HeI/H2\; fo
 r dwarfs\, HII component is important because intergalactic radiation ioni
 zes HI\, as N.Gnedin noted). Conducting calculations is hard and requires 
 assumptions and/or modeling. In $[1{]}$ slope $b \\approx 3$ was obtained 
 for 32 spirals ($V_{\\rm flat} \\approx 45...280$ km/s\; HII mass was not 
 estimated). Slope $b = 2$ appears in modeling [2\;App.G] (luminosity is sq
 uare of mass\, $L_{\\rm gal} \\approx M_{\\rm gal}^2$\, except for dwarfs)
 . This slope prefers (large scale) gravity force $F \\sim M_{\\rm bar}/R$\
 ; some authors called it MOGA\, MOdified Gravity Attraction\, $[3]$. MOGA 
 appears also in one 5$D$-variant of Teleparallelism with $4^{\\rm th}$-ord
 er gravity and expanding brane-universe [4]: Newton's law turns to $F(R) =
  GMm/(LR)$ when $R > L$ ($L$ is the brane co-moving thickness along the ex
 tra-dimension). As it is stated in $[3]$\, MOGA\, unlike MOND\, preserves 
 the momentum and angular momentum\, as well as stability of three-body sys
 tems. \n\nLet's consider large scales\, $R > L$. For thin disks (SO${}_2$-
 symmetry\; plain $1/R$-model)\, the force in the disk plane at radius $R$\
 , $F(R)$\, depends on the mass $M_R$ inside this radius:  $ F = G m M_R /(
 LR)$\; on the axis $Z$ (uniform disc of radius $a$\; 'test-mass' $m$) the 
 attraction force is  \n$ \\ \\ F(Z) = G m M_a Z \\ln(1 + a^2/Z^2) /(L a^2)
 . \\\\  $ \n$ \\ \\ {\\rm For}$ uniform spherical balls (bulges\; radius $
 a$)\, we find: \n$\\ \\ F(R) = G mM /(L a) \\ \\\,  f (R/a) \, {\\rm \\ wh
 ere  } \\\\$\n $ \\ \\ \\ \\ f (x) = \\frac38 \\{1/x + x\\\, –\\frac12 (
 1/x\\\, – x)^2 \\ln[(x + 1)/|x\\\, – 1|]\\}\;$\n it is maximal at  $x 
 = 1$\,  $f (1) = 3/4. \\\\ $\nThis function is symmetrical for the substit
 ution $x → 1/x$\, so similar series exist for small and large $x$: $\\\\
  $ \n             $ \\ \\ \\ \\    f (x) = x\\{1 – x^2/5 – … – 3 x
 ^{2n}/[(2n – 1)(2n + 1)(2n + 3)] – …\\} = 1/x\\{1 – 1/(5x^2) – 
 … \\} . \\\\$\nOne can further integrate (in parts) this function and fi
 nd the potential:$\\\\ $\n                $\\ \\ \\  \\ u(x) = \\int\\! f 
 (y)\\\, d y = \\frac12 \\ln|x^2 – 1| + \n\\frac{x^2}8 – \\frac{x^4 –
  6x^2 – 3}{16x} \\ln \\frac{x + 1}{|x – 1|} + C$.\n\n   Logarithmic po
 tential growth stops when «underdensities» appear\, and cosmic voids sho
 uld be objects with negative masses. Our MW galaxy resides in the KBC void
  (one among the largest – redshift z is small) with a shift from its cen
 ter. Defocusing caused by the KBC void provides some extra-dipoles (redshi
 ft dependent). Further we are considering a simple model of spherical void
 s with a massive shell\, which consists of two co-centered uniform balls w
 ith positive and negative densities\, $\\rho_b$ and $–\\rho_a$\, of radi
 us $b$ and $a$\, respectively.\nLet the total shell mass is  $M_S = \\rho_
 b V_b – \\rho_a V_a  =  \\rho_0 V_b$\, where $\\rho_0 \\sim 0.04 \\rho_c
 $  is the mean baryonic density of the Universe. And take\, for simplicity
 \,  $\\rho_b  = \\rho_a$  (an absolutely empty void)\, and  $b = \\varepsi
 lon\\\, a$  (with\, say\, $\\varepsilon  = 1.1$). One can can find the fol
 lowing  void potential (again\,  $x = r/a$)\n            $  \\    U(x) = G
 M_S L^{-1} \\\, u^*(x)$\, where  \n$ \\    u^*(x) = [u(x/\\varepsilon ) 
 – u(x)]/(\\varepsilon^3 – 1)$.  \nWe took into account that the unifor
 m density  $\\rho_0$  gives no gravity\, no potential  (the case $a → 0$
 ). \nFor very thin shells\,  $a → b$ and \n$\\varepsilon  → 1$\, we fi
 nd  $ u^*(x) → – x f (x)/3$ and repulsion \nis ${\\propto} (x f' + f)/
 3$. \n\n1. Ponomareva A.A. et al. From light to baryonic mass: the effect 
 of the stellar mass-to-light ratio on the Baryonic Tully–Fisher relation
  // MNRAS. 2018. V.474. 4366. [hal-02117129f][2] \n2. Valageas P.\, Schaef
 fer R. The mass and luminosity functions of galaxies and their evolution /
 / Astron. Astrophys. 1999. V. 345\, 329\;\n arXiv: astro-ph/9812213. \n3. 
 Toxvaerd S. Approximations and modifications of celestial dynamics tested 
 on the three-body system. arXiv:2512.03823 [gr-qc] \n(see also arXiv:2403.
 02848 [astro-ph.GA]). \n4. Zhogin I.L. Longitudinal waves in 5D Absolute P
 arallelism and relativistically expanding brane cosmology // Space\, Time 
 & Fund. Inter. 2025. No.2. 40 (Rus.\; stfi.ru/en/\; also see [sciforum.net
 /paper/28941][3])\n\n\n  [1]: https://darkmattercrisis.wordpress.com/\n  [
 2]: https://hal.science/hal-02117129v1/document\n  [3]: http://sciforum.ne
 t/paper/28941\n\nhttps://indico.particle.mephi.ru/event/626/contributions/
 6455/
LOCATION:Sevastopol hotel Conference Hall 1
URL:https://indico.particle.mephi.ru/event/626/contributions/6455/
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