Post-linear Schwarzschild solution in harmonic coordinates: Elimination of structure-dependent terms
Post-linear Schwarzschild solution in harmonic coordinates: Elimination of structure-dependent terms
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DOI：
10.1103/physrevd.89.104056
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发表时间：
2014-02
影响因子：
5
通讯作者：
S. Klioner;M. Soffel
中科院分区：
文献类型：
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作者：
S. Klioner;M. Soffel
这篇论文讨论了爱因斯坦扩展体场方程解中出现的一类特殊问题：许多与结构相关的项出现在中间计算中，这些项由于局部运动方程而完全抵消，或者可以通过适当的规范变换来消除。对于静止的单个物体，这些问题在后牛顿和后闵可夫斯基的情况下都可以很好地理解。然而，对于高阶近似，情况仍不清楚。本文针对球对称到后线性阶的“体”讨论这个问题。我们明确地证明了如何直接从调和规范中的后线性近似中的场方程以及任意球对称物质分布中导出通常的史瓦西场。外部和内部解决方案均被考虑。然后将静态不可压缩流体的情况与文献中众所周知的结果进行比较。本文的结果可以应用于推广后线性近似中著名的后牛顿和后闵可夫斯基度量的多极展开式。
The paper deals with a special kind of problems that appear in solutions of Einstein's field equations for extended bodies: many structure-dependent terms appear in intermediate calculations that cancel exactly in virtue of the local equations of motion or can be eliminated by appropriate gauge transformations. For a single body at rest these problems are well understood for both the post-Newtonian and the post-Minkowskian cases. However, the situation is still unclear for approximations of higher orders. This paper discusses this problem for a "body" of spherical symmetry to post-linear order. We explicitly demonstrate how the usual Schwarzschild field can be derived directly from the field equations in the post-linear approximation in the harmonic gauge and for an arbitrary spherically symmetric matter distribution. Both external and internal solutions are considered. The case of static incompressible fluid is then compared to the well-known results from the literature. The results of this paper can be applied to generalize the well-known post-Newtonian and post-Minkowskian multipole expansions of the metric in the post-linear approximation.