We have succeeded in obtaining highly relativistic structures of stationary axisymmetric configurations consisting of massive complex scalar fields, i.e., rotating boson stars. Scalar fields are assumed to have harmonic azimuthal angular dependence, i.e., $\phi ={\phi }_0(t,r,\theta )e^{\mathrm{im}\phi }$, where $m$ is an integer. Equilibrium configurations are characterized by values of $m$ so that the total angular momentum of the boson star becomes discrete. We have solved sequences of equilibrium states with $m=1\mathrm{}$ and $m=2\mathrm{}$ by changing one parameter which characterizes the model. The maximum mass for $m=1\mathrm{}$ models is ${1.314M}_{\mathrm{Pl}}^2/\mu$, where $M_{\mathrm{Pl}}$ and $\mu$ are the Planck mass and the mass of the scalar field, respectively. It is interesting that properly defined specific angular momentum for rotating boson stars is constant in space.

• Received 5 March 1997

DOI:https://doi.org/10.1103/PhysRevD.56.762