Extended gravitational vortex without dark matter

Abstract

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.