  Within the framework of the theory of strongly-interacting quantum Bose
liquids, we consider a general relativistic model of self-interacting complex
scalar fields with logarithmic nonlinearity taken from dense superfluid models.
We demonstrate the existence of gravitational equilibria in this model,
described by spherically symmetric nonsingular finite-mass asymptotically-flat
solutions. These equilibrium configurations can describe both massive
astronomical objects, such as bosonized superfluid stars or cores of neutron
stars, and finite-size particles and non-topological solitons, such as Q-balls.
We give an estimate for masses and sizes of such objects.
