The two generalized solutions for the stationary axisymmetric vacuum garvitational field

Abstract

In this paper by applying Ehlers transformation to Schwarzschild and Kerr soluti ons of Ernst equation and introducing the proper coordinate transformations, the two solutions of the Ernst equation, i.e., the so called generalized NUT-Taub ( GNT) solution and generalized Kerr-NUT (GKN) solution are obtained, which not on ly can reduce to the well-known Schwarzschild and Kerr solutions when the parame ter L=0, but also can also reduce to the NUT-Taub metric and Kerr-NUT metric res pectively when the parameter LM and if taking 1-LM2≈1. It is showe d that in the NUT-Taub and Kerr-NUT solutions the range of value for the paramet er l (interpreted as the gravomagnetic monopole) can't be arbitrary and should be limited by mass of the source to |l|M.