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arXiv · 1907.05659

Extended bodies moving on geodesic trajectories

Sajal Mukherjee·Georgios Lukes-Gerakopoulos·Rajesh Kumble Nayak
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Abstract

This work investigates whether an extended test body obeying the Mathisson-Papapetrou- Dixon equations under the Ohashi-Kyrian-Semerak 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-Semerak 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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Sajal Mukherjee, Georgios Lukes-Gerakopoulos, Rajesh Kumble Nayak. 2019-07-12. Extended bodies moving on geodesic trajectories. https://doi.org/10.1007/s10714-022-02985-6

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