Soliton boson stars, Q-balls and the causal Buchdahl bound
  Self-gravitating non-topological solitons whose potential admits multiple
vacua are promising candidates for exotic compact objects. Such objects can
arise in several extensions of the Standard Model and could be produced in the
early Universe. In this work, we focus on objects made from complex scalars
(gravitating Q-balls/soliton boson stars), deriving analytic solutions in
spherical symmetry and comparing them with fully numerical ones. In the
high-compactness limit we find that these objects present an effectively linear
equation of state, thus saturating the Buchdahl limit with the causality
constraint. Far from that limit, these objects behave either as flat space-time
Q-balls or (in the low-compactness limit) as mini boson stars stabilized by
quantum pressure. We establish the robustness of this picture by analyzing a
variety of potentials (including cosine, quartic and sextic ones).
