Evolution of the Schrödinger-Newton system for a self-gravitating scalar field

Using numerical techniques, we study the collapse of a scalar field configuration in the Newtonian limit of the spherically symmetric Einstein-Klein-Gordon system, which results in the so called Schr\"odinger-Newton (SN) set of equations. We present the numerical code developed to evolve the SN system and related topics, like equilibrium configurations and boundary conditions. Also, we analyze the evolution of different initial configurations and the physical quantities associated with them. In particular, we readdress the issue of the gravitational cooling mechanism for Newtonian systems and find that all systems settle down onto a zero-node equilibrium configuration.