NEW SOURCES FOR KERR AND OTHER METRICS - ROTATING RELATIVISTIC DISCS WITH PRESSURE SUPPORT

Complete sequences of new analytic solutions of Einstein's equations w hich describe thin supermassive discs are constructed. These solutions are derived geometrically. The identification of points across two sy mmetrical cuts through a vacuum solution of Einstein's equations defin es the gradient discontinuity from which the properties of the disc ca n be deduced. The subset of possible cuts which lead to physical solut ions is presented. At large distances, all these discs become Newtonia n but in their central regions they exhibit relativistic features such as velocities close to that of light, and large redshifts. Sections w ith zero extrinsic curvature yield cold discs. Curved sections may ind uce discs which are stable against radial instability. The general cou nter-rotating flat disc with planar pre;sure tensor is found, Owing to gravomagnetic forces, there is no systematic method of constructing v acuum stationary fields for which the non-diagonal component of the me tric is a free parameter. However, all static vacuum solutions may be extended to fully stationary fields via simple algebraic transformatio ns. Such discs can generate a great variety of different metrics, incl uding Kerr's metric with any ratio of a to m. A simple inversion formu la is given, which yields all distribution functions compatible with t he characteristics of the flow, providing formally a complete descript ion of the stellar dynamics of flattened relativistic discs. It is ill ustrated for the Kerr disc.