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We adopt a generic form that parametrizes the components of $c_{\\mu\\nu}$ in terms of one four-vector, namely, $c_{\\mu\\nu}=u_\\mu u_\\nu - \\zeta \\frac{u^2}{4}g_{\\mu\\nu}$. We then generate perturbatively, up to the third order in this tensor, the aether-like term for the gauge field. 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