  We study the gravitational effect of non-self-annihilating dark matter on
compact stellar objects. The self-interaction of condensate dark matter can
give high accretion rate of dark matter onto stars. Phase transition to
condensation state takes place when the dark matter density exceeds the
critical value. A compact degenerate dark matter core is developed and alter
the structure and stability of the stellar objects. Condensate dark matter
admixed neutron stars is studied through the two-fuid TOV equation. The
existence of condensate dark matter deforms the mass-radius relation of neutron
stars and lower their maximum baryonic masses and radii. The possible effects
on the Gamma-ray Burst rate in high redshift are discussed.
