  Recently, Morishima, Futamase and Shimizu published a series of manuscripts,
putting forward arguments, based on a post-Newtonian approximative calculation,
that there can be a sizable general relativistic (GR) correction in the
experimental determination of the muon magnetic moment based on spin
precession, i.e., in muon g-2 experiments. In response, other authors argued
that the effect must be much smaller than claimed. Further authors argued that
the effect exactly cancels. Also, the known formulae for de Sitter and
Lense-Thirring effect do not apply due to the non-geodesic motion. All this
indicates that it is difficult to estimate from first principles the influence
of GR corrections in the problem of spin propagation. Therefore, in this paper
we present a full general relativistic calculation in order to quantify this
effect. The main methodology is the purely differential geometrical tool of
Fermi-Walker transport over a Schwarzschild background. Also the Larmor
precession due to the propagation in the electromagnetic field of the
experimental apparatus is included. For the muon g-2 experiments the GR
correction turns out to be very small, well below the present sensitivity.
However, in other similar storage ring experimental settings, such as electric
dipole moment (EDM) search experiments, where the so-called frozen spin method
is used, GR gives a well detectable effect, and should be corrected for. All
frozen spin scenarios are affected which intend to reach a sensitivity of 0.1
microradians/second for the spin precession in the vertical plane.
