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

By F. S. Guzmán, L. Arturo Ureña‐López. 2004

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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 Schrodinger-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. PACS numbers: 04.40.-b, 98.35.Jk, 98.62.Gq I. INTRODUCTION In a previous paper of ours(1), we studied the forma- tion of a gravitationally bounded object comprised of scalar particles, under the influence of Newtonian gravity. The dynamics of the system is described by the coupled Schrodinger-Newton (SN) system of equations, which is nothing but the weak field limit of its general relativistic counterpart, the Einstein-Klein-Gordon (EKG) system. As at the moment we have no hints to finding an an- alytic solution for the evolution, we found necessary to develop numerical techniques to study the formation pro- cess of the scalar objects. The study of the dynami- cal properties of the fully time-dependent SN system has been done before in the literature(2, 3, 4, 5), but more is needed in order to understand the gravitational collapse of a weakly gravitating scalar field. The main aim of this paper is to perform an exhaustive numerical study of the collapse and evolution of a spher- ically symmetric scalar object in the Newtonian regime. Here, we develop a numerical strategy to evolve the SN system, and study important issues like the stability and the formation process of gravitationally bound scalar sys- tems, a topic that has recently become attractive in Cos- mology (1, 2, 5, 6, 7, 8, 9). A summary of the paper is as follows. In Sec. II, we present the relativistic EKG and Newtonian SN equa- tions that describe the evolution of a self-gravitating scalar field in the spherically symmetric case. Corre- spondingly, it is described how the EKG and the SN

Subfields: Astronomy and Astrophysics, Mathematical Physics, Nuclear and High Energy Physics

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Citations in the corpus

Axion dark matter, solitons and the cusp–core problem (2015, result): “(A46) These values are in agreement with those reported in table II of Guzman & Urena-Lopez (2004), who studied an equivalent system.”
Angular Momentum and Vortex Formation in Bose-Einstein-Condensed Cold Dark Matter Haloes (2011, methodology): “For some discussion of this dynamical evolution, the reader is referred to Alcubierre et al. (2002); Guzmán & Ureña-López (2004) and Short & Coles (2006).”
Ultralight scalars as cosmological dark matter (2016, methodology): “Following other authors [41, 57, 95, 96, 190, 191] we compute numerically the solutions of these equations, and label the eigenstates n = 0, 1, 2, · · · in order of increasing energy.”
Flat central density profiles from scalar field dark matter halos (2003, background): “However, as pointed out in Guzmán and UreñaLópez 2005 (see also Guzmán and Ureña-López 2004), this last proposal cannot be realistic because Sabbathicak leave at Max-Planck-Institut für Gravitationsphysik, Albert Einstein Institut, 14476 Golm, Germany.”
Gravitational Cooling of Self-gravitating Bose Condensates (2006, methodology): “The virialization and stabilization of physical configurations evolving according to equations (1) and (2) with ¼ 0 was first proposed in Seidel & Suen (1994), and revised in detail in Guzmán & Ureña-López (2004).”