Static axisymmetric rings in general relativity: How diverse they are

Understand

Three static and axially symmetric (Weyl-type) ring singularities -- the Majumdar-Papapetrou--type (extremally charged) ring, the Bach-Weyl ring and the Appell ring -- are studied in general relativity in order to show how remarkably the geometries in their vicinity differ from each other.

• This is demonstrated on basic measures of the rings and on invariant characteristics given by the metric and by its first and second derivatives (lapse, gravitational acceleration and curvature), and also on geodesic motion.
• The results are also compared against the Kerr space-time which possesses a ring singularity too.
• The Kerr solution is only stationary, not static, but in spite of the consequent complication by dragging, its ring appears to be simpler than the static rings.