Extended bodies moving on geodesic trajectories
arXiv:1907.05659 · doi:10.1007/s10714-022-02985-6
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.
28 pages, no figure. v2, title changed, new author added, revised version
References in corpus (10)
- A gravito-electromagnetic analogy based on tidal tensors
- Spinning particles in general relativity: Momentum-velocity relation for the Mathisson-Pirani spin condition
- Investigating spinning test particles: spin supplementary conditions and the Hamiltonian formalism
- Bobbing and Kicks in Electromagnetism and Gravity
- Frame-dragging effect in the field of non rotating body due to unit gravimagnetic moment
- Quadrupole effects on the motion of extended bodies in Kerr spacetime
- Spin gauge symmetry in the action principle for classical relativistic particles
- Off-equatorial stable circular orbits for spinning particles
- Extended-body motion in black hole spacetimes: What is possible?
- Extended bodies in a Kerr spacetime: exploring the role of a general quadrupole tensor