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We study the stability of rotating scalar boson stars, comparing those madefrom a simple massive complex scalar (referred to as mini boson stars), tothose with several different types of nonlinear interactions. To that end, wenumerically evolve the nonlinear Einstein-Klein-Gordon equations in 3D,beginning with stationary boson star solutions. We show that the linear,non-axisymmetric instability found in mini boson stars with azimuthal number$m=1$ persists across the entire parameter space for these stars, though thetimescale diverges in the Newtonian limit. Therefore, any boson star with $m=1$that is sufficiently far into the non-relativistic regime, where the leadingorder mass term dominates, will be unstable, independent of the nonlinearscalar self-interactions. However, we do find regions of $m=1$ boson starparameter space where adding nonlinear interactions to the scalar potentialquenches the non-axisymmetric instability, both on the non-relativistic, andthe relativistic branches of solutions. We also consider select boson starswith $m=2$, finding instability in all cases. For the cases exhibitinginstability, we follow the nonlinear development, finding a range of dynamicsincluding fragmentation into multiple unbound non-rotating stars, and formationof binary black holes. Finally, we comment on the relationship betweenstability and criteria based on the rotating boson star's frequency in relationto that of a spherical boson star or the existence of a co-rotation point. Theboson stars that we find not to exhibit instability when evolved for manydynamical times include rapidly rotating cases where the compactness iscomparable to that of a black hole or neutron star.

Stability of rotating scalar boson stars with nonlinear interactions