The gravitomagnetic clock effect

The gravitomagnetic clock effect is the difference in periods of a test par ticle revolving in prograde and retrograde circular geodesic orbits around a rotating body. We study this effect far a cylindrically symmetric system, but our analysis also applies to orbits around the Kerr source in its plan e of symmetry. The effect depends on the coordinate system, and we find the condition that it can be reduced to zero by a suitable choice of rotating axes. We apply our formulae to the van Stockum metric for a rotating dust cylinde r, and to the Kerr solution. In the former there is a gravitomagnetic clock effect only in the case of low mass per unit length, and the coordinate sy stem in which the effect vanishes is the one in which the distant stars wou ld be at rest. In Kerr spacetime the gravitomagnetic clock effect can be ma de to vanish, but only by choosing a frame rotating with respect to the dis tant stars.