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 axisymmetric discs in closed forms. We show that these results can be used to construct infinite sequences of new solutions of Einstein's equations which describe counter-rotating static discs of finite mass. At large distances these discs become Newtonian, but in their central regions they exhibit relativistic features such as velocities close to that of light and large redshifts. In particular, we construct space-times representing relativistic Kuzmin-Toomre discs and Kalnajs-Mestel discs; the second family includes also the relativistic generalization of the isochrone discs. The properties of the discs are discussed and illustrated.