  Defining the electric and magnetic field vectors in curved spacetime requires
a proper choice of the observer's frame four-vector. Related literature shows
that this fundamental issue in physics still needs to be properly resolved. In
recent literature on using electromagnetic means to detect gravitational waves,
an ad hoc definition based on regarding $F_{ab}$ with two covariant indices as
the special relativistic one is popular. We show that by assigning physical
fields to tensor components in that way, one cannot identify the frame
four-vector allowing such a choice, thus failing to properly define the
external charge and current densities in that frame. We propose the normal
frame as the proper one. In this frame, the weak gravity corrections appear as
the effective polarizations and magnetizations in both the homogeneous and
inhomogeneous parts of Maxwell equations.
