Abstract
The recent developments in particle physics and cosmology suggest that scalar fields may have played an important role in the evolution of the early Universe and that they may make up part of the missing dark matter. If so, scalar particles may be found in the Universe as diffuse gas clouds, as compact objects-boson stars-or mixed up with baryonic matter and thus even be present in ordinary stars. We give an overview of the present knowledge on gravitational equilibrium configurations of scalar fields-boson stars-in the framework of a Newtonian and of a general relativistic treatment. The mixed boson-fermion stars are also discussed. The main properties of the boson star, such as total mass and size, depend on the mass of the constituent scalar fields and on the types of interaction, besides gravity, they are subject to. We discuss also the dynamical stability of boson stars and of mixed boson-fermion stars and for the former their formation through gravitational instabilities.
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