用微分方程近似对称性确定引力波能量含量的建议
A Proposal for Determining the Energy Content of Gravitational Waves by Using Approximate Symmetries of Differential Equations
摘要：
由于引力波时空是爱因斯坦场方程随时间变化的真空解，因此没有明确的方法来定义它们的能量含量。然而，韦伯和惠勒已经证明，它们确实会给测试粒子带来能量。有各种各样的建议来定义能量含量，但它们都没有取得很大的成功。在这里，我们提出了一个定义，使用“轻微破碎”的Noether对称性。我们检查这个定义在物理上是否可以接受。所采用的程序是呼吁“近似对称性”中定义的李分析和使用它们的限制的确切对称举行。一个问题是注意到使用的建议，平面前的引力波。为了更好地理解这一建议的含义，我们还使用人工构建的时变非真空度规，并评估其外尔和应力能量张量，以便分别获得引力和物质分量，并将它们与我们的建议获得的能量含量进行比较。该方法也适用于柱面引力波解。这个定义的有用性通过它引出了关于引力波是否具有自阻尼的一个结果而得到了证明。
英文摘要：
Since gravitational wave spacetimes are time-varying vacuum solutions of Einstein's field equations, there is no unambiguous means to define their energy content. However, Weber and Wheeler had demonstrated that they do impart energy to test particles. There have been various proposals to define the energy content but they have not met with great success. Here we propose a definition using "slightly broken" Noether symmetries. We check whether this definition is physically acceptable. The procedure adopted is to appeal to "approximate symmetries" as defined in Lie analysis and use them in the limit of the exact symmetry holding. A problem is noted with the use of the proposal for plane-fronted gravitational waves. To attain a better understanding of the implications of this proposal we also use an artificially constructed time-varying non-vacuum metric and evaluate its Weyl and stress-energy tensors so as to obtain the gravitational and matter components separately and compare them with the energy content obtained by our proposal. The procedure is also used for cylindrical gravitational wave solutions. The usefulness of the definition is demonstrated by the fact that it leads to a result on whether gravitational waves suffer self-damping.
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