Can extended bodies follow geodesic trajectories?

Proceedings of RAGtime / Can extended bodies follow geodesic trajectories?

Can extended bodies follow geodesic trajectories?

Authors

Georgios Lukes-Gerakopoulos and Sajal Mukherjee

Abstract

We provide an extension of the analysis on whether an extended test body can follow a geodesic trajectory given by Mukherjee et al. (2022). In particular, we consider a test body in a pole-dipole-quadrupole approximation under the Ohashi-Kyrian-Semerák spin supplementary condition moving in the Schwarzschild and Kerr background. Using orbital setups under which a pole-dipole body can follow geodesic motion, we explore under which conditions this can also take place in the pole-dipole-quadrupole approximation when only the mass quadrupole is taken into account. For our analysis, we employ the assumption that the dipole contribution and the quadrupole contribution vanish independently.

Keywords

Mathisson–Papapetrou–Dixon equations – particle dynamics – black holes

PDF file here

References

  1. Carter, B. (1968). Global structure of the Kerr family of gravitational fields. Physical Review, 174(5), 1559.
  2. Costa, L. F., & Natário, J. (2014). Gravitoelectromagnetic analogy based on tidal tensors. General Relativity and Gravitation, 46(12), 1792.
  3. Dixon, W. G. (1970a). Dynamics of extended bodies in general relativity I. Momentum and angular momentum. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 314(1519), 499-527.
  4. Dixon, W. G. (1970b). Dynamics of extended bodies in general relativity II. Moments of the charge-current vector. Proceedings of the Royal Society of London. Series A, Mathematical and Physical Sciences, 319(1539), 509-547.
  5. Dixon, W. G. (1974). Dynamics of extended bodies in general relativity III. Equations of motion. Philosophical Transactions of the Royal Society of London. Series A, Mathematical and Physical Sciences, 277(1264), 59-119.
  6. Harms, E., Lukes-Gerakopoulos, G., & Kunst, D. (2016). Spin and quadrupole contributions to the motion of astrophysical binaries. Physical Review D, 93(4), 043016.
  7. Kyrian, K., & Semerák, O. (2007). Spinning test particles in a Kerr field. Monthly Notices of the Royal Astronomical Society, 382(4), 1922-1932.
  8. Mathisson, M. (1937). Neue Mechanik materieller Systeme. Acta Physica Polonica, 6, 163-200.
  9. Mukherjee, S., Harms, E., Lukes-Gerakopoulos, G., Kunst, D., & Puetzfeld, D. (2022). Extended body motion and geodesic deviation in general relativity. Physical Review D, 105(2), 024042.
  10. Ohashi, A. (2003). Extended bodies in general relativity: equations of motion and their post-Newtonian approximation. Physical Review D, 68(4), 044009.
  11. Steinhoff, J., & Puetzfeld, D. (2010). Influence of internal structure on the motion of test bodies in extreme mass ratio situations. Physical Review D, 81(4), 044019.
  12. Steinhoff, J., & Puetzfeld, D. (2012). Multipolar equations of motion for extended test bodies in general relativity. Physical Review D, 86(4), 044033.