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

• Applicant: Professor Dr. Claus Lämmerzahl
• Subject Area: Nuclear and Elementary Particle Physics, Quantum Mechanics, Relativity, Fields
• Term: from 2011 to 2018
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 193896206

• Final Report Year: 2015

Final Report Abstract

Within this project we investigated the motion of structured test bodies in gravity. The results obtained span from explicit solutions of the equations of motion in General Relativity, to the development of new multipolar approximations schemes for generalized gravity theories beyond the standard relativistic framework. Within Einstein’s theory we were able to explicitly solve the equation of motion for spinning test bodies in de Sitter space-time. In particular the impact of different supplementary conditions on the motion was investigated. Building on these results we classified the motion of spinning test bodies in Kerr space-time in the equatorial plane. Furthermore, we worked out the motion of poledipole and quadrupole test bodies in Kerr geometry, and devised an explicit quadrupole model, which includes spin and tidal interactions. With the help of this model we determined the influence of internal structure on the motion of test bodies. Our results in complement recent investigations of the conservative part of the self-force of bodies in extreme mass ratio situations. In the context of generalized gravitational theories established a very general unified covariant multipolar framework for test bodies. This was achieved by a series of works, and in particular by a thorough study of the conservation laws in generalized gravity theories. The derived framework is applicable to large classes of gravitational theories, even encompassing a possible nonminimal coupling to matter, and allows for the systematic test of theories which go beyond Einstein’s theory of gravitation. In particular our results provide a description of extended and microstructured test bodies in post-Riemannian space-times. Consequently we applied our findings to several popular gravitational theories including scalar-tensor theories, Poincaré gauge theory of gravity, metric-affine gravity, as well as nonminmal extensions of these theories. By means of our framework, we were able to demonstrate in a very general context, that it is only possible to detect the post-Riemannian space-time geometry by ordinary (non-microstructured) test bodies if gravity is nonminimally coupled to matter. This result has direct consequences for the measurability of new space-time features by means of present and future experiments. In particular, we showed in detail, that space-time torsion cannot be detected in minimally coupled theories by the analysis of the GP-B experiment, as was erroneously claimed in the literature. However, by means of our general results we were also able to show that there might be a loophole to detect non-Riemannian space-time features, for example torsion, macroscopically. This is a peculiar feature which we found for certain subclasses of nonminimal theories. This sensitivity to post-Riemannian space-time structures even in experiments without microstructured test matter may be exploited in the future analysis of experiments.

Publications

• Influence of internal structure on the motion of test bodies in extreme mass ratio situations, Phys. Rev. D 86 (2012) 044033
  Jan Steinhoff, Dirk Puetzfeld
  
• Conservation laws in gravitational theories with general nonminimal coupling, Phys. Rev. D 87 (2013) 081502(R)
  Yuri N. Obukhov, Dirk Puetzfeld
  
• Covariant equations of motion for test bodies in gravitational theories with general nonminimal coupling, Phys. Rev. D 87 (2013) 044045
  Dirk Puetzfeld, Yuri N. Obukhov
  
• Equations of motion in gravity theories with nonminimal coupling: a loophole to detect torsion macroscopically?, Phys. Rev. D 88 (2013) 064025
  Dirk Puetzfeld, Yuri N. Obukhov
  
• On Poincaré gauge theory of gravity, its equations of motion, and Gravity Probe B, Phys. Lett. A 377 (2013) 1775
  Friedrich W. Hehl, Yuri N. Obukhov, Dirk Puetzfeld
  
• Conservation laws in gravity: A unified framework, Phys. Rev. D 90 (2014) 024004
  Yuri N. Obukhov, Dirk Puetzfeld
  
• Equations of motion in metric-affine gravity: a covariant unified framework, Phys. Rev. D 90 (2014) 084034
  Dirk Puetzfeld, Yuri N. Obukhov
  
• Equations of motion in scalar-tensor theories of gravity: A covariant multipolar approach, Phys. Rev. D 90 (2014) 104041
  Yuri N. Obukhov, Dirk Puetzfeld
  
• Motion of spinning test bodies in Kerr spacetime, Phys. Rev. D 90 (2014) 064035
  E. Hackmann, C. Lämmerzahl, Y.N. Obukhov, D. Puetzfeld, I. Schaffer