Exact Relativistic Gravitational Field of a Stationary Counterrotating Dust Disk

We present a solution to the Ernst equation which represents an infinitesimally thin dust disk consisting of two streams of particles circulating with constant angular velocity in opposite directions. These streams have the same density distribution but their relative density may vary continuously. In the limit of only one component of dust, we get the solution for the rigidly rotating dust disk of Neugebauer and Meinel; in the limit of identical densities, the static disk of Morgan and Morgan is obtained. We discuss the Newtonian and the ultrarelativistic limit, the occurrence of ergospheres, and the regularity of the solution.