Boson Stars as Gravitational Lenses
  We discuss boson stars as possible gravitational lenses and study the lensing effect by these objects made of scalar particles. The mass and the size of a boson star may vary from an individual Newtonian object similar to the Sun to the general relativistic size and mass of a galaxy close to its Schwarzschild radius. We assume boson stars to be transparent which allows the light to pass through them though the light is gravitationally deflected. We assume boson stars of the mass $M = 10^{10}M_\odot$ to be on non-cosmological distance from the observer. We discuss the lens equation for these stars as well as the details of magnification. We find that there are typically three images of a star but the deflection angles may vary from arcseconds to even degrees. There is one tangential critical curve (Einstein ring) and one radial critical curve for tangential and radial magnification, respectively. Moreover, the deflection angles for the light passing in the gravitational field of boson stars can be very large (even of the order of degrees) which reflects the fact they are very strong relativistic objects. We also propose a suitable formula for the lens equation for such large deflection angles, and with the reservation that large deflection angle images are highly demagnified but in the area of the tangential critical curve, their existence may help in observational detection of suitable lenses possessing characteristic features of boson stars which could also serve as a direct evidence for scalar fields in the universe. 
Mariusz P. Dabrowski and Franz E. Schunck