Models of rotating boson stars and geodesics around them: New type of orbits

We have developed a highly accurate numerical code capable of solving the coupled Einstein-Klein-Gordon system, in order to construct rotating boson stars in general relativity. Free fields and self-interacting fields, with quartic and sextic potentials, are considered. In particular, we present the first numerical solutions of rotating boson stars with rotational quantum number $k=3$ and $k=4$, as well as the first determination of the maximum mass of free-field boson stars with $k=2$. We have also investigated timelike geodesics in the spacetime generated by a rotating boson star for $k=1$, 2 and 3. A numerical integration of the geodesic equation has enabled us to identify a peculiar type of orbit: the zero-angular-momentum ones. These orbits pass very close to the center and are qualitatively different from orbits around a Kerr black hole. Should such orbits be observed, they would put stringent constraints on astrophysical compact objects like the Galactic center.