  In this work we study the effects of non-minimal coupling between
electromagnetism and gravity, which are motivated by quantum effects such as
vacuum polarization. We investigate the modification of both asymptotically
dipole and uniform magnetic fields around a Schwarzschild black hole that come
as the result of non-minimal coupling. While in both cases the magnetic field
gets enhanced or suppressed with respect to the case of minimal coupling,
depending on the sign of non-minimal coupling parameter, in the case of a
background uniform magnetic field the direction of the magnetic field also
alters in the vicinity of the black hole horizon. We have discussed the
possible astrophysical and cosmological sources for which the vacuum
polarization may be at play, while also discussing the observational effects,
in particular the possibility of synchrotron radiation from the vicinity of a
black hole. We conclude that such observations could be used to constrain the
value of the non-minimal coupling parameter.
