Spinning test body orbiting around a Kerr black hole: Comparing spin supplementary conditions for circular equatorial orbits

Abstract

This work discusses the motion of extended test bodies as described by the Mathisson-Papapetrou-Dixon (MPD) equations in the pole-dipole-quadrupole approximation. We focus on the case that the quadrupole is solely induced by the spin of the body which is assumed to move on a circular equatorial orbit in a Kerr background. To fix the center of mass of the MPD body we use two different spin supplementary conditions (SSCs): the Tulczyjew-Dixon SSC and the Mathisson-Pirani SSC. We provide the frequencies of the circular equatorial orbits for the pole-dipole-(spin induced) quadrupole approximation of the body for both SSCs. In the process we develop an explicit fourvelocity four-momentum relation for a pole-dipole-quadrupole body under the Mathisson-Pirani SSC.

Charged spinning and magnetized test particles orbiting quantum improved charged black holes

“…Ladino and Larrañaga study the motion of spinning test particles around an improved rotating black hole [45], where using the Mathisson-Papapetrou*** -Dixon (MPD) equations and the Tulczyjew spin supplementary condition, the authors investigated the equatorial circular orbits, finding that the event horizon and the radius of the Innermost Stable Circular Orbit (ISCO) for the quantum-improved rotating black hole are smaller than Schwarzschild and Kerr classi-cal solutions. The dynamics of spinning test particles have called the attention of the community, and several works consider different spacetime backgrounds [45][46][47][48][49][50][51][52][53][54][55][56][57][58][59][60][61][62][63]. In this manuscript, we consider the motion of charged spinning test particle motion around quantum-improved charged black holes; we also study the dynamics of magnetized test particles.…”