The purpose of this paper is to get second-order gravitational equations, a correction made to Jefimenko’s linear gravitational equations. These linear equations were first proposed by Oliver Heaviside in [1], making an analogy between the laws of electromagnetism and gravitation. To achieve our goal, we will use perturbation methods on Einstein field equations. It should be emphasized that the resulting system of equations can also be derived from Logunov’s non-linear gravitational equations, but with different physical interpretation, for while in the former gravitation is considered as a deformation of space-time as we can see in [2,3,4,5], in the latter gravitation is considered as a physical tensor field in the Minkowski space-time (as in [6,7,8]). In Jefimenko’s theory of gravitation, exposed in [9, 10], there are two kinds of gravitational fields, the ordinary gravitational field, due to the presence of masses, at rest, or in motion and other field called Heaviside field due to and acts only on moving masses. The Heaviside field is known in general relativity as Lense-Thirring effect or gravitomagnetism (The Heaviside field is the gravitational analogous of the magnetic field in the electromagnetic theory, its existence was proved employing the Gravity Probe B launched by NASA (See, for example, [11, 12]). It is a type of gravitational induction), interpreted as a distortion of space-time due to the motion of mass distributions, (see, for example [13, 14]). Here, we will present our second-order Jefimenko equations for gravitation and its solutions.

中文翻译：

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后牛顿极限：二阶Jefimenko方程

本文的目的是获得二阶引力方程，这是对杰斐明科的线性引力方程的修正。这些线性方程是由Oliver Heaviside在[1]中首先提出的，它在电磁定律和引力定律之间作了类比。为了实现我们的目标，我们将对爱因斯坦场方程使用摄动方法。应该强调的是，方程组的最终结果也可以从Logunov的非线性引力方程组导出，但是具有不同的物理解释，因为在前一种情况下，引力被认为是时空的变形，正如我们在[2]中看到的那样。 ，3,4,5]，在后一种情况下，重力被认为是Minkowski时空中的物理张量场（如[6,7,8]）。[9，10]中揭露了叶捷明科的引力理论，引力场有两种，一种是普通的引力场，由于存在质量而处于静止状态，或者处于运动状态；其他场称为Heaviside场，由于它仅作用于运动的质量而起作用。Heaviside场在广义相对论中称为Lense-Thirring效应或重力磁场（Heaviside场是电磁理论中磁场的引力类似物，通过使用NASA发射的重力探测器B（例如，参见[11，12]）。它是一种重力感应，被解释为由于质量分布运动而引起的时空扭曲（例如，参见[13，14]）。在这里，我们将介绍引力的二阶Jefimenko方程及其解。