New sources for Kerr and other metrics: rotating relativistic discs with pressure support

Complete sequences of new analytic solutions of Einstein's equations whichdescribe thin super massive disks are constructed. These solutions are derivedgeometrically. The identification of points across two symmetrical cuts througha vacuum solution of Einstein's equations defines the gradient discontinuityfrom which the properties of the disk can be deduced. The subset of possiblecuts which lead to physical solutions is presented. At large distances, allthese disks become Newtonian, but in their central regions they exhibitrelativistic features such as velocities close that of light, and largeredshifts. Sections with zero extrinsic curvature yield cold disks. Curvedsections may induce disks which are stable against radial instability. Thegeneral counter rotating flat disk with planar pressure tensor is found. Owingto gravomagnetic forces, there is no systematic method of constructing vacuumstationary fields for which the non-diagonal component of the metric is a freeparameter. However, all static vacuum solutions may be extended to fullystationary fields via simple algebraic transformations. Such disks can generatea great variety of different metrics including Kerr's metric with any ratio ofa to m. A simple inversion formula is given which yields all distributionfunctions compatible with the characteristics of the flow, providing formally acomplete description of the stellar dynamics of flattened relativistic disks.It is illustrated for the Kerr disk.