Gravitational Lensing by Boson Stars

Boson stars can be gravitational lenses in a similar way as other astrophysical objects (Dabrowski & Schunck 2000). They can be transparent which allows the light to pass through them and to be gravitationally deflected. We discuss the lens equation for these stars as well as the details of magnification assuming they are on non-cosmological distance from the observer and that their mass is M = 10¹⁰M_⊙. We find that there are typically three images of a star. There is one tangential critical curve (Einstein ring) and one radial critical curve for tangential and radial magnification, respectively. The deflection angles for the light moving in the gravitational field of boson stars can be very large (even of the order of degrees) which means that they are very strong relativistic objects. We derive an analytic formula for the lens equation applied 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 in observational detection of suitable lenses possessing characteristic features of boson stars which could serve as a direct evidence for scalar fields in the universe...