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Extended bodies moving on geodesic trajectories

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Abstract

This work investigates whether an extended test body obeying the Mathisson–Papapetrou–Dixon equations under the Ohashi–Kyrian–Semerák  spin supplementary condition can follow geodesic trajectories in curved spacetimes. In particular, we explore what are the requirements under which pole-dipole and pole-dipole-quadrupole approximated bodies moving in the Schwarzschild or Kerr spacetimes can follow equatorial geodesic trajectories. We do this exploration thoroughly in the pole-dipole case, while we focus just on particular trajectories in the pole-dipole-quadrupole case. Using the Ohashi–Kyrian–Semerák  spin supplementary condition to fix the center of the mass of a pole-dipole body has the advantage that the hidden momentum is eliminated. This allows the four-velocity to be parallel to the four-momentum, which provides a convenient framework for our investigation. We discuss how this feature can be recovered at a pole-dipole-quadrupole approximation and what are the consequences.

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Notes

  1. A similar phenomenon also appears in electrodynamics, and for details, we refer our readers to Refs.  [20, 21, 23, 33].

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Acknowledgements

S.M. wish to acknowledge Narayan Banerjee for some useful interactive sessions at the earlier stage of this work. The authors would like to express their gratitude to L. Filipe O. Costa for the clarification he has provided and for pointing out some important consequences of the present work. They would also like to thank the Inter-University Centre for Astronomy and Astrophysics (IUCAA), Pune, India, where parts of this work were carried out during academic visits. The authors wish to thank the referees for their constructive criticism on the article. S.M. and G.L.-G. have been supported by the fellowship Lumina Quaeruntur No. LQ100032102 of the Czech Academy of Sciences.

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Authors and Affiliations

  1. Department of Physical Sciences, IISER-Kolkata, Mohanpur, 741246, India

    Sajal Mukherjee & Rajesh Kumble Nayak

  2. Astronomical Institute of the Czech Academy of Sciences, Bocni II 1401/1a, 14100, Prague, Czech Republic

    Sajal Mukherjee & Georgios Lukes-Gerakopoulos

  3. Center of Excellence in Space Sciences India, IISER-Kolkata, Mohanpur, India

    Rajesh Kumble Nayak

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  1. Sajal Mukherjee
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Mukherjee, S., Lukes-Gerakopoulos, G. & Nayak, R.K. Extended bodies moving on geodesic trajectories. Gen Relativ Gravit 54, 113 (2022). https://doi.org/10.1007/s10714-022-02985-6

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