Using the fully nonlinear and exact perturbation formulation with magnetohydrodynamics (MHD) in the Minkowski background, we derive first-order, post-Newtonian (1PN) equations without imposing the slicing (temporal gauge) condition. The 1PN-MHD formulation is complementary to our recently presented fully relativistic MHD combined with 0PN gravity available only in the maximal slicing. We present the 1PN-MHD equations in two gauge conditions previously used in the literature and provide gauge transformation relations between different gauges. We derive the PN effects on MHD waves in a static homogeneous medium.

中文翻译：

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牛顿后修正的磁流体动力学

在Minkowski背景中使用具有磁流体动力学（MHD）的完全非线性且精确的扰动公式，我们导出了一阶牛顿后（1PN）方程，而没有施加切片（时间尺度）条件。1PN-MHD公式是对我们最近提出的完全相对论MHD和仅在最大切片中可用的0PN重力的补充。我们介绍了先前在文献中使用过的两个量规条件下的1PN-MHD方程，并提供了不同量规之间的量规转换关系。我们推导了在静态均质介质中PN对MHD波的影响。