具有伽利略协变性的后牛顿展开
Post-Newtonian expansion with Galilean covariance
摘要：
伽利略引力是由标量势和矢量势导出的。确定标量势的泊松方程不具有期望的伽利略协方差。此外，有三个失踪的方程来确定潜在的矢量。此外，我们要求它们具有伽利略协方差。这些都是本文要讨论的问题。为了避免PPN方法和NCT的缺点，我们将它们合并到一个新的框架中。关键思想是要注意场的c展开式的每一项都是伽利略协变或不变量。期望的方程推导出的希尔伯特-爱因斯坦泛函的变化。物质对泛函的贡献来自Souriau的构象张量。我们得到一个系统的四个非线性方程，解决了渐近展开。
英文摘要：
The Galilean gravitation derives from a scalar potential and a vector one. Poisson's equation to determine the scalar potential has no the expected Galilean covariance. Moreover, there are three missing equations to determine the potential vector. Besides, we require they have the Galilean covariance. These are the issues addressed in the paper. To avoid the drawbacks of the PPN approach and the NCT, we merge them into a new framework. The key idea is to take care that every term of the c expansion of the fields are Galilean covariants or invariants. The expected equations are deduced by variation of the Hilbert-Einstein functional. The contribution of the matter to the functional is derived from Souriau's conformation tensor. We obtain a system of four non linear equations, solved by asymptotic expansion.
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