New sources for Kerr and other metrics: rotating relativistic discs with pressure support
Abstract
Complete sequences of new analytic solutions of Einstein's equations which describe thin supermassive discs are constructed. These solutions are derived geometrically. The identification of points across two symmetrical cuts through a vacuum solution of Einstein's equations defines the gradient discontinuity from which the properties of the disc can be deduced. The subset of possible cuts which lead to physical solutions is presented. At large distances, all these discs become Newtonian but in their central regions they exhibit relativistic features such as velocities close to that of light, and large redshifts. Sections with zero extrinsic curvature yield cold discs. Curved sections may induce discs which are stable against radial instability. The general counterrotating flat disc with planar pressure tensor is found. Owing to gravomagnetic forces, there is no systematic method of constructing vacuum stationary fields for which the nondiagonal component of the metric is a free parameter. However, all static vacuum solutions may be extended to fully stationary fields via simple algebraic transformations. Such discs can generate a great variety of different metrics, including Kerr's metric with any ratio of a to m. A simple inversion formula is given, which yields all distribution functions compatible with the characteristics of the flow, providing formally a complete description of the stellar dynamics of flattened relativistic discs. It is illustrated for the Kerr disc.
 Publication:

Monthly Notices of the Royal Astronomical Society
 Pub Date:
 June 1996
 DOI:
 10.1093/mnras/280.4.1007
 arXiv:
 arXiv:astroph/9605037
 Bibcode:
 1996MNRAS.280.1007P
 Keywords:

 RELATIVITY;
 METHODS: ANALYTICAL;
 CELESTIAL MECHANICS;
 STELLAR DYNAMICS;
 QUASARS: GENERAL;
 Astrophysics
 EPrint:
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