微扰法解Einstein场方程

Solving Einstein's Field Equations by Perturbation

首先从已知具有对角型度规的Einstein场方程的精确解出发,近似推导了含有微扰条件下的场方程形式;其次,利用这一微扰形式具体计算了静态球对称引力场的外部微扰解,并进而讨论了球状星系外部的引力特征.结果表明,该微扰解不仅可以与内部解衔接,而且在消除微扰的情况下还可以自动恢复到Schwarzchild解的形式.

From a diagonal metric tensor depending on four coordinates, the perturbation formulation of Einstein＇s equations is deduced firstly. And second, based on this formulation the perturbation solutions of Einstein＇s equations in global stationary axisymmetric fields are calculated. It shows that, in the case of no perturbation existing, the Schwarzchild^s solutions can be recovered naturally. Finally, the reasonableness of the perturbation solutions is discussed, which can help people to understand the gravitational properties of the globular cluster surrounded by faint gaseous shells.