The Galilean gravitation derives from a scalar potential and a vector one. Poisson’s equation to determine the scalar potential has not 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.

中文翻译：

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广义相对论的渐近展开与伽利略协方差

伽利略引力来自标量势和矢量势。用于确定标量势的泊松方程没有预期的伽利略协方差。此外，还缺少三个确定潜在向量的方程。此外，我们要求它们具有伽利略协方差。这些都是论文中要解决的问题。为了避免 PPN 方法和 NCT 的缺点，我们将它们合并到一个新框架中。关键思想是注意域的 c 展开的每一项都是伽利略协变量或不变量。通过 Hilbert-Einstein 泛函的变化推导出预期方程。物质对泛函的贡献来源于 Souriau 的构象张量。我们得到了一个由四个非线性方程组成的系统，通过渐近展开式求解。