Boson Stars with Large Self-interaction in (2+1) dimensions: an Exact Solution

An exact solution for a nonrotating boson star in (2+1) dimensional gravity with a negative cosmological constant is found. The relations among mass, particle number, and radius of the (2 + 1) dimensional boson star are shown. PACS number(s): 04.20.Jb, 04.40.Dg Typeset using REVTEX ∗e-mail: [email protected], [email protected] 1 Self-gravitating systems have been investigated in various situations. Boson stars ( [1] [2] for reviews) have a very simple constituent, a complex scalar field which is bound by gravitational attraction. Thus the boson star provides the simplest model of relativistic stars. The solutions for relativistic boson stars are only numerically obtained in four dimensions. In (2 + 1) dimensions, static equilibrium configurations have been argued [3] in Einstein gravity with a negative cosmological constant. In this paper, we obtain an exact solution for a nonrotating boson star in (2+ 1) dimensional gravity with a negative cosmological constant. We consider that the scalar field has a strong self-interaction. An infinitely large self-interaction term in the model leads to much simplications as in the (3+1) dimensional case [4]. The study of exact solutions will lead to a new aspect of gravitating systems and clarify the similarity and/or the difference among the other dimensional cases. We consider a complex scalar field with mass m and a quartic self-coupling constant λ. The action for the scalar field coupled to gravity can be written down as S = ∫