Boson stars as gravitational lenses

We discuss boson stars as possible gravitational lenses and study the lensing effect of these objects made up 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, although the light is gravitationally deflected. Ne assume boson stars of mass M = 10(10) M(circle dot), to be on noncosmological distance from the observer. We discuss the lens equation for these stars as well as the details of magnification. Ne 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 through the gravitational held of boson stars can be very large (even of the order of degrees), which reflects the fact that they are very strong relativistic objects. We derive a suitable formula for the lens equation for such large deflection angles. Although the large deflection angle images are highly demagnified, their existence in the area of the tangential critical curve may help with 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.