We present a method for constructing equilibrium disks with net angular mom
entum in general relativity. The method solves the relativistic Vlasov equa
tion coupled to Einstein's equations for the gravitational field. We apply
the method to construct disks that are relativistic versions of Newtonian K
alnajs disks. In Newtonian gravity these disks are analytic and are stable
against ring formation for certain ranges of their velocity dispersion. We
investigate the existence of fully general relativistic equilibrium sequenc
es for differing values of the velocity dispersion. These models are the fi
rst rotating, relativistic disk solutions of the collisionless Boltzmann eq
uation.