Among known finite-mass nonspherical solutions of Einstein's equations few have physical sources. We show that most vacuum Weyl solutions can arise as the metrics of counter-rotating relativistic disks. We give the metric for the general counter-rotating relativistic disk and show how the Curzon, Schwarzschild, Zipoy-Vorhees, and Israel-Kahn metrics can be generated by the disks. The physical properties of the disks are discussed and illustrated. The central gravitational redshift can become arbitrarily large. The disks with new metrics are discussed elsewhere.

• Received 19 October 1992

DOI:https://doi.org/10.1103/PhysRevD.47.4334