RELATIVISTIC DISKS AND FLAT GALAXY MODELS

Recent progress in Newtonian potential theory of infinitesimally thin discs enables one to generate the potential-density pairs of axisymmet ric discs in closed forms. We show that these results can be used to c onstruct infinite sequences of new solutions of Einstein's equations w hich describe counter-rotating static discs of finite mass. At large d istances these discs become Newtonian, but in their central regions th ey exhibit relativistic features such as velocities close to that of l ight and large redshifts. In particular, we construct space-times repr esenting relativistic Kuzmin-Toomre discs and Kalnajs-Mestel discs; th e second family includes also the relativistic generalization of the i sochrone discs. The properties of the discs are discussed and illustra ted.