关于稳态轴对称真空引力场方程的两个扩展解

The two generalized solutions for the stationary axisymmetric vacuum garvitational field

将Ehlers变换应用于Ernst方程的Schwarzschild解和Kerr解,通过引入Boyer-Lindquist坐标变换以及相关的参数代换,得到了Ernst方程的两个扩展解.当所含参数L=0时,其中一个扩展解退化为Schwarzschild解,另一个退化为Kerr解.当参数|L|M时,如果取近似1-ML2≈1,则这两个扩展解分别退化为已知的NUT-Taub解和Kerr-NUT解.这一结果表明NUT-Taub解和Kerr-NUT解中所含的参数l并非能任意取值,它的取值要受到引力源质量M的限制,即要求|l|M.

In this paper by applying Ehlers transformation to Schwarzschild and Kerr solutions 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 only can reduce to the well-known Schwarzschild and Kerr solutions when the parameter L = 0, but also can also reduce to the NUT-Taub metric and Kerr-NUT metric respectively when the parameter L〈〈 M and if taking 1 -（L/M）^2≈1. It is showed that in the NUT - Taub and Kerr-NUT solutions the range of value for the parameter l （interpreted as the gravomagnetic monopole） can＇t be arbitrary and should be limited by mass of the source to ｜l｜〈〈 M.