Two boson stars in equilibrium

We construct and explore the solution space of two nonspinning, miniboson stars in equilibrium, in fully nonlinear general relativity (GR), minimally coupled to a free, massive, complex scalar field. The equilibrium is due to the balance between the (long range) gravitational attraction and the (short-range) scalar mediated repulsion, the latter enabled by a g relative phase. Gravity is mandatory; it is shown no similar solutions exist in flat spacetime, replacing gravity by nonlinear scalar interactions. We study the variation of the proper distance between the stars with their mass (or oscillation frequency), showing it can be qualitatively captured by a simple analytic model that features the two competing interactions.