Clock effect due to gravitational spin-orbit coupling

In this Letter, we consider a possible gravitational spin-orbit coupling. It is shown that in presence of such a coupling there would appear a clock effect very similar to the gravitomagnetic clock effect. The new clock effect is found to be topological. According to this effect, two counter-orbiting spinning test particles placed on two identical, circular equatorial orbits around a central massive body would take different times to complete a full revolution. We obtain, in this Letter, a qualitative expression for the period difference.