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Flow generation via catastrophic loss of equilibrium in weakly rotating self-gravitating fluids: A minimal idealized model

L. Gudushauri*

N. L. Shatashvili†

G. Shekiladze‡

S. M. Mahajan§

  • Department of Physics, Faculty of Exact and Natural Sciences, Ivane Javakhishvili Tbilisi State University (TSU), Tbilisi 0179, Georgia and Andronikashvili Institute of Physics, TSU, Tbilisi 0177, Georgia

  • *Contact author: lasha.ghudushauri28@gmail.com
  • †Contact author: nana.shatashvili@tsu.ge
  • ‡Contact author: gshekiladze@ufl.edu
  • §Contact author: mahajan@mail.utexas.edu
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Phys. Rev. E 113, 025102 – Published 13 February, 2026

DOI: https://doi.org/10.1103/whwv-trcw

Abstract

This paper explores the catastrophic energy transformations, in particular the ones leading to the generation of a flow in a weakly rotating self-gravitating fluid/gas found, for instance, in the vicinity of a massive compact object. Because of the similarity in the governing equations, the system dynamics is worked out exactly in parallel to the methods developed for investigating catastrophic relaxation in stellar plasmas [S. Ohsaki et al., Astrophys. J. 559, L61 (2001); Astrophys. J. 570, 395 (2002); E. Saralidze et al., Astrophys. Space Sci. 370, 64 (2025)]. In the latter, a more “complex” equilibrium state, on slow changes in the environment, can lose its equilibrium (catastrophe), and transform to a less complex state with a very different energy mix from the original. It is shown that a similar transformation in the weakly rotating self-gravitating fluid/gas will convert much of its gravitation energy into kinetic energy in the flow. Since flows are a perennial ingredient of high-energy astrophysical systems, the energy transformation processes revealed in the present study, can advance our understanding of a variety of them. Some particularly relevant examples are macroscale flows / structures in galaxies, accretion discs, and the dynamics and stability of a rotating star / its atmosphere.

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References (39)

  1. M. C. Begelman, R. D. Blandford, and M. D. Rees, Rev. Mod. Phys. 56, 255 (1984).
  2. M. C. Begelman, Conference summary, in Astrophysical Jets, ed. D. Burgarella, et al. (Cambridge University Press, Cambridge, 1993), pp. 305–315.
  3. R. D. Blandford and M. J. Rees, Mon. Not. R. Astron. Soc. 169, 395 (1974).
  4. G. V. Ustyogova, A. V. Koldova, M. M. Romanova, V. M. Chechetkin, and R. V. E. Lovelace, Astrophys. J. 516, 221 (1999).
  5. C. P. Dullemond, D. Hollenbach, I. Kamp, and P. D'Alessio, in Protostars and Planets, edited by B. Reipurth, D. Jewitt, and K. Keil (Arizona University Press, Tucson, AZ, 2007), p. 555.
  6. E. Katsadze, N. Revazashvili, and N. L. Shatashvili. J. High Energy Astrophys. 43, 20 (2024).
  7. S. Ohsaki, N. L. Shatashvili, Z. Yoshida, and S. M. Mahajan, Astrophys. J. 559, L61 (2001).
  8. S. Ohsaki, N. L. Shatashvili, S. M. Mahajan, and Z. Yoshida, Astrophys. J. 570, 395 (2002).
  9. E. Saralidze, N. L. Shatashvili, S. M. Mahajan, and E. Dadiani, Astrophys. Space Sci. 370, 64 (2025).
  10. S. M. Mahajan, N. L. Shatashvili, S. V. Mikeladze, and K. I. Sigua, Astrophys. J. 634, 419 (2005); Phys. Plasmas 13, 062902 (2006).
  11. W.-H. Lei, B. Zhang, and H. Gao, Astrophys. J. 762, 98 (2013).
  12. V. Venkatraman Krishnan, M. Bailes, W. van Straten, N. Wex, P. C. C. Freire, E. F. Keane, T. M. Tauris, P. A. Rosado, N. D. R. Bhat, C. Flynn, et al., Science 367, 577 (2020).
  13. C. J. Bhattacharjee, J. Plasma Phys. 88, 175880101 (2022).
  14. C. T. Sebens, Br. J. Philos. Sci. 73, 211 (2022).
  15. N. L. Shatashvili and Z. Yoshida, AIP Conf. Proc. 1392, 73 (2011).
  16. S. M. Mahajan and Z. Yoshida, Phys. Rev. Lett. 81, 4863 (1998).
  17. Z. Yoshida and S. M. Mahajan, J. Math. Phys. 40, 5080 (1999).
  18. Z. Yoshida, S. M. Mahajan, S. Ohsaki, M. Iqbal, and N. L. Shatashvili, Phys. Plasmas 8, 2125 (2001).
  19. S. M. Mahajan, R. Miklaszewski, K. I. Nikol'skaya, and N. L. Shatashvili, Phys. Plasmas 8, 1340 (2001).
  20. O. Heaviside, Electrician 31, 281 (1893).
  21. K. S. Thorne, R. H. Price, and D. A. MacDonald, Black Holes: The Membrane Paradigm (Yale University Press, 1986).
  22. K. S. Thorne, Gravitomagnetism, jets in quasars, and the stanford gyroscope experiment, in Near Zero: New Frontiers of Physics, edited by, J. D. Fairbank, B. S. Deaver Jr., C. W. F. Everitt, and P. F. Michelson (W. H. Freeman and Company, New York, 1988).
  23. V. B. Braginsky, C. M. Caves, and K. S. Thorne, Phys. Rev. D 15, 2047 (1977).
  24. G. Manfredi, Gen. Relat. Gravit. 47, 1 (2015).
  25. G. Manfredi, J. Phys. 34, 4 (2013).
  26. C. Bhattacharjee, Phys. Rev. E 112, 045206 (2025).
  27. A. A. Barnaveli and N. L. Shatashvili, Astrophys. Space Sci. 362, 164 (2017).
  28. S. M. Mahajan, K. I. Nikol'skaya, N. L. Shatashvili, and Z. Yoshida, Z. Astro. Phys. J. 576, L161 (2002).
  29. We remind the reader that for multifluid plasmas each Beltrami condition is an alignment of a vorticity and a corresponding flow velocity. Our system consists of only one neutral fluid, hence, we have only one velocity v of this fluid locally, at the same time, we have a so called gravito-magnetic field (Bg≠0 due to self-gravity taken into account, κ≠0) and, as shown above, the flow vorticity is generalized [see (7)]; also we have only one Beltrami paramater b. Then, the derived equation (10) is of higher order (DB-like); without this effect (leading to κ→0) we would get the single Beltrami (SB) equation for the flow (see the details of derivation in [13]). We can, however, mathematically analyze our self-gravitating flow as a DB system—flow generalized by self-gravity—and follow the methodology developed for the exploxive/erruptive events.
  30. S. M. Mahajan and Y. Yoshida, Phys. Plasmas 7, 640 (2000).
  31. L. C. Steinhauer and A. Ishida, Phys. Rev. Lett. 79, 3423 (1997).
  32. V. I. Arnold and B. A. Khesin, Topological Methods in Hydrodynamics, Applied Mathematical Sciences, Vol. 125 (Springer Science+Business Media, New York, Berlin, Heidelberg, 1998).
  33. N. I. Shakura and R. A. Sunyaev, Astron. Astrophys. 24, 337 (1973).
  34. E. ArshilavaGogilashvili, M. Gogilashvili, V. Loladze, I. Jokhadze, B. Modrekiladze, N. L. Shatashvili Tevzadze, and A. G. Tevzadze, J. High Energy Astrophysics. 23, 6 (2019).
  35. M. Lingam and S. M. Mahajan, Mon. Not. R. Astron. Soc. 449, L36 (2015).
  36. K. Kotorashvili, N. Revazashvili, N. L. Shatashvili, Astrophys. Space. Sci. 365, 175 (2020).
  37. K. Kotorashvili and N. L. Shatashvili, Astrophys. Space. Sci. 367, 2 (2022).
  38. D. Kagan, S. M. Mahajan, Mon. Not. R. Astron. Soc. 406, 1140 (2010).
  39. S. M. Tobias, K. Dagon, and J. B. Marston, Astrophys. J. 727, 127 (2011).

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Phys. Rev. E 113, 025102– Published 13 February, 2026
  • Received 10 September 2025
  • Accepted 28 January 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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