  [Abridged] Context. The Galactic Center supermassive black hole is well known
to exhibit transient peaks of flux density on a daily basis across the
spectrum. Recent infrared and millimeter observations have strengthened the
case for the association between these flares and circular orbital motion in
the vicinity of the event horizon. The strongly polarized synchrotron radiation
associated with these events leads to specific observables called QU loops,
that is, looping motion in the Stokes QU plane of linear polarization. Aims. We
want to deepen the understanding of the QU loops associated with orbiting hot
spots. We compute such loops in Minkowski and Schwarzschild spacetimes in order
to determine which aspects of the observed patterns are due to special- or
general-relativistic phenomena. Results. We show that QU loops in Minkowski
spacetime at low or moderate inclination i < 45 deg share all qualitative
features of Schwarzschild QU loops: there exist QU loops for all setups
considered (including face-on view and vertical magnetic field), there may be
one or two QU loops per orbital period for a vertical magnetic field
configuration, there are always two QU loops in case of a toroidal magnetic
field. We provide analytical formulas in Minkowski spacetime to explain the
details of this behavior. Moreover, we analyze the flux variation of the hot
spot and show that it is dictated either by the angular dependence of the
radiative transfer coefficients, or by relativistic beaming. In the former
case, this can lead to extreme flux ratios even at moderate inclination.
Finally, we highlight the increasing mirror asymmetry of the Schwarzschild QU
track with increasing inclination and show that this behavior is a specific
Schwarzschild feature caused by light bending.
