Motion in a central field with account of dark matter

Abstract

Motion in a central gravitational field in the presence of dark matter is considered. A macroscopic description of dark matter via a longitudinal vector field with as simple a Lagrangian as possible allows for describing the observable manifestations of dark matter analytically. Expressions for galaxy rotation curves and the light refractive index are obtained in terms of observable parameters—the rotation rate on the plateau and the period of damped oscillations. Within the plateau (where the velocities of circulating stars are independent of the radius), the refractive index of a ray does not depend on the impact parameter.