Exact relativistic treatment of stationary counter-rotating dust disks II: Axis, Disk and Limiting Cases

摘要

This is the second in a series of papers on the construction of explicitsolutions to the stationary axisymmetric Einstein equations which can beinterpreted as counter-rotating disks of dust. We discuss the class ofsolutions to the Einstein equations for disks with constant angular velocityand constant relative density which was constructed in the first part. Themetric for these spacetimes is given in terms of theta functions on a Riemannsurface of genus 2. We discuss the metric functions at the axis of symmetry andthe disk. Interesting limiting cases are the Newtonian limit, the static limit,and the ultra-relativistic limit of the solution in which the central redshiftdiverges.