  Electromagnetic moments of particles carry important information on their
internal structure, as well as on the structure of the effective Lagrangian
describing their underlying field theory. One of the cleanest observable of
such kind is the electric dipole moment (EDM), since Standard Model estimates
would imply very small, much less then 10^-30 ecm value for that quantity,
whereas several Beyond Standard Model (BSM) theories happen to predict of the
order of 10^-28 ecm EDM for elementary or hadronic particles. So far, precision
EDM upper bounds are mainly available for neutrons via cold neutron
experiments, and indirect measurements for electrons. Therefore, in the recent
year there has been a growing interest for direct measurement of EDM for
charged particles, such as electrons, protons, muons or light nuclei. Such
measurements become possible in relativistic storage rings, called frozen spin
storage rings. Many environmental factors give systematic backgrounds to the
EDM signal, including General Relativity (GR), due to the gravitational field
of the Earth. It turns out that, depending of the experimental scenario, the GR
effect can be well above the planned EDM sensitivity. Therefore, it is both of
concern as a source of systematics, as well as it can serve as a spin-off
experiment for an independent test of GR. There are a handful of theoretical
papers quantifying the GR systematics, delivering slightly different results.
The aim of this paper is to clarify these claims, eventually try to reconcile
these predictions, and to deduce their experimental implications. The closing
section of the paper quantifies the field imperfection systematic error
cancellation in the case of a so-called doubly-frozen spin storage ring
setting, in the idealized axial symmetric limit.
