Not yet reviewed by Pith; the record is open.

We investigate the structure and stability properties of compact astrophysical objects that may be formed from the Bose-Einstein condensation of dark matter. Once the critical temperature of a boson gas is less than the critical temperature, a Bose-Einstein Condensation process can always take place during the cosmic history of the universe. Therefore we model the dark matter inside the star as a Bose-Einstein condensate. In the condensate dark matter star model, the dark matter equation of state can be described by a polytropic equation of state, with polytropic index equal to one. We derive the basic general relativistic equations describing the equilibrium structure of the condensate dark matter star with spherically symmetric static geometry. The structure equations of the condensate dark matter stars are studied numerically. The critical mass and radius of the dark matter star are given by $M_{crit}\approx 2(l_a/1fm)^{1/2}(m_{\chi}/1\;{\rm GeV})^{-3/2}M_{\odot}$ and $R_{crit}\approx 1.1 \times 10^6(l_a/1\;{\rm fm})^{1/2}(m_{\chi}/1\;{\rm GeV})^{-3/2}$ cm respectively, where $l_a$ and $m_{\chi}$ are the scattering length and the mass of dark matter particle, respectively.