Received September 3, 2020, published online December 25, 2020
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.