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Can extended bodies follow geodesic trajectories?
Lukes-Gerakopoulos, Georgios ; Mukherjee, Sajal
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-Semer´ak 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 independentlly.

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