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We study the properties of ultra-compact spherically symmetric dark mattersector star objects, being the solution of Einstein equations with two$U(1)$-gauge fields. One of them is the ordinary Maxwell field, while theauxiliary gauge field pertains to the hidden sector, and mimics the propertiesof dark matter. The visible and hidden sectors are coupled by a kinetic mixingterm with a coupling constant $\alpha$. We also investigate the possibility ofcondensation of charged scalar field around the reflecting dark matter starobject. It happens that dark matter sector, both dark matter charge andcoupling constant, cause shrinking of the star radius for which thecondensation may occur.

Ultra-compact spherically symmetric dark matter charged star objects