Constraints on the non-minimal coupling of electromagnetic field from
  astrophysical observations
  Non-minimal coupling between the Riemann curvature and the electromagnetic
field appears as quantum corrections when gravity is coupled to the standard
model of particle physics. The non-minimal coupling is expected to be dominant
in the strong-gravity regions such as near black-holes or the early Universe.
With better instruments planned shortly, electromagnetic fields are an
important source of astrophysical observations to test general relativity in
strong gravity regimes. However, to precisely test general relativity in strong
gravity using electromagnetic fields, it is \emph{imperative} to obtain
constraints on the non-minimal coupling parameter to electromagnetic fields. As
a step in this direction, we calculate the deflection angle of non-minimally
coupled electromagnetic fields in the vicinity of a dynamical, spherically
symmetric black hole described by the Sultana-Dyer metric. We compare the
deflection angle of the photon modes for the Sultana-Dyer black hole with the
Schwarzschild black hole. We show that the difference in the deflection angle
for the Schwarzschild black hole is always negative, while for Sultana-Dyer is
always positive. Thus, our analysis points out that the two black holes provide
a distinct signature irrespective of the black hole mass. We discuss the
implications of the results for future astrophysical observations.
