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Non-minimal coupling between the Riemann curvature and the electromagneticfield appears as quantum corrections when gravity is coupled to the standardmodel of particle physics. The non-minimal coupling is expected to be dominantin the strong-gravity regions such as near black-holes or the early Universe.With better instruments planned shortly, electromagnetic fields are animportant source of astrophysical observations to test general relativity instrong gravity regimes. However, to precisely test general relativity in stronggravity using electromagnetic fields, it is \emph{imperative} to obtainconstraints on the non-minimal coupling parameter to electromagnetic fields. Asa step in this direction, we calculate the deflection angle of non-minimallycoupled electromagnetic fields in the vicinity of a dynamical, sphericallysymmetric black hole described by the Sultana-Dyer metric. We compare thedeflection angle of the photon modes for the Sultana-Dyer black hole with theSchwarzschild black hole. We show that the difference in the deflection anglefor the Schwarzschild black hole is always negative, while for Sultana-Dyer isalways positive. Thus, our analysis points out that the two black holes providea distinct signature irrespective of the black hole mass. We discuss theimplications of the results for future astrophysical observations.

Constraints on the non-minimal coupling of electromagnetic field from astrophysical observations