We use an orthonormal frame approach to provide a general framework for the first order hyperbolic reduction of the Einstein equations coupled to a fairly generic class of matter models. Our analysis covers the special cases of dust and perfect fluid. We also provide a discussion of self-gravitating elastic matter. The frame is Fermi-Walker propagated and coordinates are chosen such as to satisfy the Lagrange condition. We show the propagation of the constraints of the Einstein-matter system.

中文翻译：

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各种爱因斯坦物质系统的演化方程

我们使用正交框架方法为爱因斯坦方程的一阶双曲线约简提供了一个通用框架，该方程与一类相当通用的物质模型耦合。我们的分析涵盖了灰尘和完美流体的特殊情况。我们还讨论了自引力弹性物质。该框架是费米-沃克传播的，并且选择坐标以满足拉格朗日条件。我们展示了爱因斯坦物质系统约束的传播。