On The Stationary Axisymmetric Vacuum Gravitational Field Equations, Two Of The Nut-like Solution And Its Spatial And Temporal Nature

In this paper By applying Ehlers transformation to Schwarzschildand Kerr solutions of Ernst equation and chosing the suitable coordinate trans-formations, the two NUT-like solutions, i.e., the so called the NUT-Taub-likeand the Kerr-NUT-like solutions are obtained which not only can respectivelyreduce to Schwarzschild and Kerr solutions when the parameter = 0, butalso can also reduce to the NUT-Taub metric and Kerr-NUT metric respec-tively when satisfies the some approximation. Meanwhile it is showed that inthe NUT-Taub and Kerr-NUT solutions the range of value for the parameterinterpreted as the gravomagnetic monopole can't be arbitrary and should beconfined by mass of the source to | | m. Furthermore, the di?erences in thegeometrical structure between the NUT-Taub-Like and NUT-Taub solutionsare discussed and some properties of the Kerr-NUT-Like solution are studied,which include the surface of infinite redshift, horizons, ergospheres and singu-larities of this solution.