  We study the gravitational Bose-Einstein condensation of a massive vector
field in the kinetic regime and the non-relativistic limit using non-linear
dynamical numerical methods. Gravitational condensation leads to the
spontaneous formation of solitons. We measure the condensation time and growth
rate, and compare to analytical models in analogy to the scalar case. We find
that the condensation time of the vector field depends on the correlation
between its different components. For fully correlated configurations, the
condensation time is the same as that for a scalar field. On the other hand,
uncorrelated or partially correlated configurations condense slower than the
scalar case. As the vector soliton grows, it can acquire a net spin angular
momentum even if the total spin angular momentum of the initial conditions is
zero.
