Charged spinning particles on circular orbits in the Reissner-Nordstr\"om spacetime

The behaviour of charged spinning test particles moving along circular orbits in the equatorial plane of the Reissner-Nordstr\"om spacetime is studied in the framework of the Dixon-Souriau model completed with standard choices of supplementary conditions. The gravitomagnetic " clock effect", i.e. the delay in the arrival times of two oppositely circulating particles as measured by a static observer, is derived and discussed in the cases in which the particles have equal/opposite charge and spin, the latter being directed along the $z$-axis.