Gravitating Q-balls in the Affleck-Dine mechanism

We investigate how gravity affects ''Q-balls'' with the Affleck-Dine potential VAD(φ):=(m2/2)φ2 [1+Kln((φ/M))2]. Contrary to the flat case, in which equilibrium solutions exist only if K<0, we find three types of gravitating solutions as follows. In the case that K<0, ordinary Q-ball solutions exist; there is an upper bound of the charge due to gravity. In the case that K=0, equilibrium solutions called (mini-)boson stars appear due to gravity; there is an upper bound of the charge, too. In the case that K>0, equilibrium solutions appear, too. In this case, these solutions are not asymptotically flat but surrounded by Q-matter. These solutions might be important in considering a dark matter scenario in the Affleck-Dine mechanism.