Spacetime Geometry of Rotating Boson Stars and KBH

The theory of a complex scalar field minimally coupled to gravity allows for amusing stationary configurations that defy common intuition built upon our knowledge of more conservative compact objects. Upon rotation, the topology of the scalar field changes and the solution possesses an offcenter distribution of energy density. In turn, the metric potentials behave nonmotonically with increasing radial coordinate, deviating considerably from external Kerr. In this talk we shall explore the spacetime structure of rotating boson stars (BSs) and Kerr black holes with scalar hair (KBHsSH) and address peculiar properties of circular orbits on their equatorial plane, as well as some astrophysical implications to accretion discs and inspirals. Furthermore, by attempting a fluid description of the complex scalar field, we will unveil a strange connection between a BS co-moving observer and the synchronization condition for KBHsH.