https://doi.org/10.1140/epjc/s10052-024-12585-0
Regular Article - Theoretical Physics
Extended gravitational vortex without dark matter
1
National Institute for Space Research, 12227-010, São José dos Campos, SP, Brazil
2
National Commission for Nuclear Energy, 22294-900, Rio de Janeiro, RJ, Brazil
Received:
3
January
2024
Accepted:
18
February
2024
Published online:
11
March
2024
This paper analyzes, within the extended gravitoelectromagnetic (GEM) formulation, the equilibrium of a large scale gravitational system formed by rotating dust. The force balance equation gives the rotation velocity in terms of the GEM fields. Boundary conditions for the fields are introduced using Helmholtz’s decomposition and the virtual casing principle. Hydro-gravitomagnetic Cauchy invariance is implemented to relate the fluid and gravitomagnetic field vorticities. An energy conservation equation gives the rotation velocity in terms of the gravitational field and respective boundary values. A detailed solution is calculated for the case of rotating oblate spheroids. The equilibrium is in the form of a sheared rotational vortex, without introducing dark matter. The results are consistent with the Tully–Fisher relation and the Virginia Trimble correlations.
© The Author(s) 2024
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