Exact Solutions of Einstein's Equations for Axisymmetric Gravitational Fields

Abstract

In this thesis Einstein's equations for vacuum axisymmetric, stationary, gravitational fields are considered. Five analytic solutions of these equations are presented. In each case the analytic solutions are generated by a non linear ordinary differential equation of the second order. Some particular integrals of these generating differential equations are given, resulting in some known and unknown metrics. The known. metrics are, the Kerr and the Tomimatsu-Sato class. In the derivation these known metrics are shown to have a common origin. It is further shown that they result from a parameter in the generating differential equation assuming certain eigenvalues.