The motion of structured test bodies in gravitational fields: Equitations of motion and their solutions

在广义相对论中，测试体的运动可以很好地用测地线方程来描述。严格来说，这只适用于无结构的中性点样测试体，而这在许多物理情况和观察中是合理的。然而，随着对卫星轨道和双星运动的测量精度的提高，与测试体的内部结构有关的影响- -如自旋和质量多极- -可能变得可以测量。这类具有内部结构的测试对象用多极逼近（MA）格式描述。这种描述的一个例子是所谓的mathison - papapetro - dixon （MPD）方程。在这个项目中，我们希望讨论各种MA方案，以确定物理量。我们还想描述与测试体的结构（例如角动量和质量四极杆）相关的可能影响，这可能对天体物理观测、GR和引力波模板的新测试很重要。为了做到这一点，我们喜欢对特殊情况用解析方法求解MPD方程，对更一般的情况用数值方法求解。

Within general relativity (GR) the motion of test bodies is very well described by means of the geodesic equation. This is strictly true only for structureless neutral pointlike test bodies what is justified for many physical situations and observations. However, with increasing accuracy of measurements of satellite orbits and motions of binary stars it might be possible that effects related to the internal structure of test bodies – like spin and mass multipoles – may become measurable. Such test objects with internal structure are described by means of multipolar approximation (MA) schemes. One example for such a description are the so-called Mathisson–Papapetrou–Dixon (MPD) equations. In this project we like to discuss various MA schemes in view of an identification of physical quantities. We also want to characterize possible effects related to the structure (e.g. angular momentum and the mass quadrupole) of the test bodies which may be of importance for astrophysical observations, new tests of GR and gravitational wave templates. In order to do this we like to solve the MPD equations analytically for special and numerically for more general situations.