Equilibrium of large scale rotating gravitational systems – the role of the gravitomagnetic field

Abstract The equilibrium of large scale gravitational rotating dust systems is analyzed within the extended gravitoelectromagnetic (GEM) formulation. The gravitomagnetic (GM) field establishes a rotational flow inside the dust fluid. Boundary and external field effects are introduced using Helmholtz’s decomposition theorem. The internal and external GM fields provide the force balance along the boundary surface that ensures the integrity of the self-gravitating system. In this sense the GM field plays the role of dark matter. The force balance leads to an inhomogeneous nonlinear Fredholm equation of the second kind describing the shape of the free flow boundary surface. The total enclosed mass is given by an exact expression corresponding to the baryonic Tully–Fisher law.