Spinning boson stars and Kerr black holes with scalar hair: the effect   of self-interactions
  Self-interacting boson stars have been shown to alleviate the astrophysically low maximal mass of their non-self-interacting counterparts. We report some physical features of spinning self-interacting boson stars, namely their compactness, the occurence of ergo-regions and the scalar field profiles, for a sample of values of the coupling parameter. The results agree with the general picture that these boson stars are comparatively less compact than the non-self-interacting ones. We also briefly discuss the effect of scalar self-interactions on the properties of Kerr black holes with scalar hair. 
Carlos A. R. Herdeiro and Eugen Radu and Helgi F. R\'unarsson
gr-qc