Evolution of the Schr\"odinger--Newton system for a self--gravitating scalar field

TL;DR

This paper investigates the collapse and equilibrium states of a self-gravitating scalar field in the Newtonian limit, using numerical methods to analyze the Schr"odinger--Newton system and its dynamics.

Contribution

It introduces a numerical code for evolving the Schr"odinger--Newton system and studies the evolution of initial configurations, including the gravitational cooling mechanism.

Findings

All systems settle into a 0-node equilibrium configuration.

The numerical code effectively models the collapse and equilibrium states.

Gravitational cooling is confirmed as a key process in the system's evolution.

Abstract

Using numerical techniques, we study the collapse of a scalar field configuration in the Newtonian limit of the spherically symmetric Einstein--Klein--Gordon (EKG) 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 topics related, like equilibrium configurations and boundary conditions. Also, we analyze the evolution of different initial configurations and the physical quantities associated to them. In particular, we readdress the issue of the gravitational cooling mechanism for Newtonian systems and find that all systems settle down onto a 0--node equilibrium configuration.