Abstract
We find new spherically symmetric charged boson star solutions of a complex scalar field coupled nonminimally to gravity by a ``John-type'' term of Horndeski theory, that is a coupling between the kinetic scalar term and Einstein tensor. We study the parameter space of the solutions and find two distinct families according to their position in parameter space. More widespread is the family of solutions (which we call branch 1) existing for a finite interval of the central value of the scalar field starting from zero and ending at some finite maximal value. This branch contains as a special case the charged boson stars of the minimally coupled theory. In some regions of parameter space we find a new second branch (``branch 2'') of solutions which are more massive and more stable than those of branch 1. This second branch exists also in a finite interval of the central value of the scalar field, but its end points (either both or in some cases only one) are extremal Reissner-Nordstr\"om black hole solutions.
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