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In this paper we show that a free electromagnetic field living in Minkowski spacetime generates an effective Weitzenbock or an effective Lorentzian spacetime whose properties aredetermined in details. These results are possible because we found using the Clifford bundle formalism the noticeable result that the energy-momentum densities of a free electromagnetic field are sources of the Hodge duals of exact 2-form fields which satisfy Maxwell like equations.

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