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

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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.