标题： 相对论天体力学与PPN参数 显示英文标题

标题： Relativistic Celestial Mechanics with PPN Parameters

摘要： 从具有两个PPN参数$\gamma$和$\beta$的全局参数化后牛顿（PPN）参考系出发，我们考虑一个有限空间的物质子系统，并为该子系统构建一个局部参考系，在该参考系中外部质量的影响仅表现为潮汐效应。 在第一后牛顿近似下，局部PPN参考系的度规张量以及全局PPN参考系与局部参考系之间的坐标变换都以显式形式构造出来。 详细讨论了反映等效原理破坏的与$\eta=4\beta-\gamma-3$成比例的项。 我们提出了一种经验性的多极矩定义，这些多极矩旨在像 Blanchet-Damour 矩在广义相对论中的作用一样，在PPN天体力学中发挥作用。 从局部PPN参考系中的度规张量出发，推导了该系统中测试粒子的平动运动方程。 对于每个具有任意多极结构的$N$扩展大质量物体的质心和自旋的平动和转动运动方程进行了推导。 作为一般运动方程的应用，考虑了一个单极-自旋偶极模型，并重新推导了已知的带有自旋的质量单极的PPN运动方程。 显示英文摘要

摘要： Starting from the global parametrized post-Newtonian (PPN) reference system with two PPN parameters $\gamma$ and $\beta$ we consider a space-bounded subsystem of matter and construct a local reference system for that subsystem in which the influence of external masses reduces to tidal effects. Both the metric tensor of the local PPN reference system in the first post-Newtonian approximation as well as the coordinate transformations between the global PPN reference system and the local one are constructed in explicit form. The terms proportional to $\eta=4\beta-\gamma-3$ reflecting a violation of the equivalence principle are discussed in detail. We suggest an empirical definition of multipole moments which are intended to play the same role in PPN celestial mechanics as the Blanchet-Damour moments in General Relativity. Starting with the metric tensor in the local PPN reference system we derive translational equations of motion of a test particle in that system. The translational and rotational equations of motion for center of mass and spin of each of $N$ extended massive bodies possessing arbitrary multipole structure are derived. As an application of the general equations of motion a monopole-spin dipole model is considered and the known PPN equations of motion of mass monopoles with spins are rederived.