The integrability issue of the Mathisson-Papapetrou equations

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Written by Georgios Lukes-Gerakopoulos

The motion of a stellar compact object around a supermassive black hole can be approximated by the motion of a spinning test particle in a Kerr spacetime background. The equations of motion of a spinning particle are given by the Mathisson-Papapetrou (MP) equations. The spin of the particle in the MP equations has to be defined with respect to a centroid. A centroid defines the wordline of the particle, and it is set by a spin supplementary condition (SSC). We shall discuss the issues arising from the existence of various SSCs, and focus on the impact they have on the integrability issue of the MP equations.