  Self-gravitating Bose-Einstein condensates (BEC) have been proposed in
various astrophysical contexts, including Bose-stars and BEC dark matter halos.
These systems are described by a combination of the Gross-Pitaevskii and
Poisson equations (the GPP system). In the analysis of these hypothetical
objects, the Thomas-Fermi (TF) approximation is widely used. This approximation
is based on the assumption that in the presence of a large number of particles,
the kinetic term in the Gross-Pitaevskii energy functional can be neglected,
yet it is well known that this assumption is violated near the condensate
surface. We also show that the total energy of the self-gravitating condensate
in the TF-approximation is positive. The stability of a self-gravitating system
is dependent on the total energy being negative. Therefore, the
TF-approximation is ill suited to formulate initial conditions in numerical
simulations. As an alternative, we offer an approximate solution of the full
GPP system.
