论文标题
重力波的分析研究
Analytical Study of Gravitational Waves
论文作者
论文摘要
本论文的目的是回顾局部完美流体源发出的重力波的分析研究的Blanchet-Damour方法。假定这些完美的流体使得可以为渐近扩展定义小参数。这种方法中的渐近扩展称为丁福后和牛顿后的扩张。通过将这些扩展插入爱因斯坦田间方程，可以获得后 - 诺顿和牛顿后方程。解决这些方程式的通常方法是使用智障和泊松积分。但是，在这些情况下，由于它们的分歧，他们无法提供任何任意秩序的解决方案。实际上，这些差异激发了Blanchet和Damour采用一种新方法来解决后诺克斯基和牛顿后方程式。他们通过特定的分析延续过程获得了通用解决方案。这些解决方案具有一些未知的术语，即如果确定，重力字段在$ \ mathbb {r}^3 $中到处都有描述。匹配程序深深地取决于分析延续，用于确定这些未知术语。
The aim of the present thesis is to review the Blanchet-Damour approach to analytical study of gravitational waves emitted by localized perfect fluid sources. It is assumed these perfect fluids are such that it is possible to define small parameters for asymptotic expansions. Asymptotic expansions in this approach are called post-Minkowskian and post-Newtonian expansions. By plugging these expansions into the Einstein field equation, post-Minkowskian and post-Newtonian equations are obtained. The usual methods for solving these equations are to use the retarded and Poisson integrals. However, they cannot provide solutions up to any arbitrary order in these cases because of their divergence. In fact, these divergences motivated Blanchet and Damour to employ a new approach to solve the post-Minkowskian and post-Newtonian equations. They obtained the general solutions by means of a specific process of analytic continuation. These solutions have some unknown terms that if one determines, the gravitational field is described everywhere in $\mathbb{R}^3$. A matching procedure, which depends deeply on analytic continuation, is used to determine these unknown terms.
