Hot, Rotating Disks in General Relativity: Collisionless Equilibrium Models

We present a method for constructing equilibrium disks with net angular momentum in general relativity. The method solves the relativistic Vlasov equation coupled to Einstein's equations for the gravitational field. We apply the method to construct disks that are relativistic versions of Newtonian Kalnajs 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 sequences for differing values of the velocity dispersion. These models are the first rotating, relativistic disk solutions of the collisionless Boltzmann equation.