Definition of electric and magnetic fields in curved spacetime

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