  We study the properties of a star made of self-gravitating bosons gas in a
mean-field approximation. A generalized set of Tolman-Oppenheimer-Volkov(TOV)
equations is derived to incorporate the effect of chemical-potential in the
general relativistic frame work. The metric-dependence of the
chemical-potential gives a new class of solutions for the boson stars. It is
demonstrated that the maximum mass and radius of the star change in a
significant way when the effect of finite chemical-potential is considered. We
also discuss the case of a boson star made of quark-condensates. It is found
that when the self-interaction between the condensates is small as compared to
their mass, the typical density is too high to form a diquark-boson star. Our
results indicate that the star of quark-condensate may be formed in a
low-density and high-pressure regime.
