标题： 依赖于调和函数的刚性旋转尘埃解 显示英文标题

标题： Rigidly rotating dust solutions depending upon harmonic functions

摘要： 我们写出适用于静止轴对称刚性旋转尘埃源的相关场方程，使得一般解依赖于椭圆方程的解和调和函数。 从偶极子Bonnor解出发，我们构建了一个渐近平坦的解，在旋转轴上有两个曲率奇点，质量发散。 除了轴上的两个点奇点外，度规在其他地方都是正则的。 最后，我们研究了一个非渐近平坦的解，具有NUT电荷和无质量环状奇点，但具有明确的质量能量表达式。 显示英文摘要

摘要： We write down the relevant field equations for a stationary axially symmetric rigidly rotating dust source in such a way that the general solution depends upon the solution of an elliptic equation and upon harmonic functions. Starting with the dipole Bonnor solution, we built an asymptotically flat solution with two curvature singularities on the rotational axis with diverging mass. Apart from the two point singularities on the axis, the metric is regular everywhere. Finally, we study a non-asymptotically flat solution with NUT charge and a massless ring singularity, but with a well-defined mass-energy expression.