The Axially Symmetric Stationary Vacuum Field Equations in Einstein's Theory of General Relativity

Abstract

All formulations of Einstein's vacuum field equations for which exact solutions have been found in the axially symmetric stationary case are compared, and the inherent restrictions of each are displayed. A measure of their usefulness as theoretical tools is gained by the ease with which they admit Kerr's (1963) solution (it being the simplest asymptotically flat metric of this kind). The solutions found using each formulation are listed and, where possible, suitably classified.