  We study properties of boson stars consisting of ultra-light scalar dark
matter with repulsive self-interactions. We investigate the origin of the
maximum mass of spherically symmetric stable stars which emerges only when
solving the full equations of motion in curved space-time, but not when solving
the approximated Schr\"odinger-Newton equations. When the repulsion is weak,
the backreaction of the curvature on the scalars acts as an additional source
of attraction and can overcome the repulsion, resulting in a maximum star mass
and compactness. We also point out that the potential in a UV completed
particle physics model of light scalar dark matter is generally more
complicated than the widely used $\phi^4$ interaction. Additional interactions
beyond $\phi^4$ in the potential can dramatically change the properties of
boson stars as well as modify the prospect of LIGO gravitational wave detection
for binary mergers of boson stars.
