  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 orbits: 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.
