Abstract
We study boson shells and boson stars in a theory of a complex scalar field coupled to the gauge field and Einstein gravity with the potential . This could be considered either as a theory of a massive complex scalar field coupled to an electromagnetic field and gravity in a conical potential, or as a theory in the presence of a potential that is an overlap of a parabolic and conical potential. Our theory has a positive cosmological constant . Boson stars are found to come in two types, having either ball-like or shell-like charge density. We studied the properties of these solutions and also determined their domains of existence for some specific values of the parameters of the theory. Similar solutions have also been obtained by Kleihaus, Kunz, Laemmerzahl and List, in a V-shaped scalar potential.
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