Solution of the geodesic equation in the induced theory of modified gravity for the case of a centrally symmetric space

The work is a continuation of a series of works in which a modified theory of induced gravity (MTIG) was proposed. The paper considers the numerical solution of the MTIG equations with a quadratic potential. Against the background of the solutions obtained for the metric of a centrally symmetric space, the equations of geodesic lines are solved for various values of the parameters. The oscillatory nature of the solutions leads to the appearance of a gravitational potential containing a spectrum of minima, and not just one, as in the Einstein theory (the Schwarzschild-de Sitter solution); and can also lead to antigravity in the second half of the period, which is expressed in the opposite acceleration of the test body. Such solutions lead to the distribution of the potential of the gravitational field, which creates an additional mass effect at large distances, which is suitable for modeling the influence of dark matter in galaxies.