Another covariant electromagnetic object is the electromagnetic stress-energy tensor, a covariant rank-2 tensor which includes the Poynting vector, Maxwell stress tensor, and electromagnetic energy density.
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This equation shows the remarkable result, called the " Kaluza miracle ", that the precise form for the electromagnetic stress-energy tensor emerges from the 5D vacuum equations as a source in the 4D equations : field from the vacuum.
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Then we need only ensure that the divergences vanish ( i . e . that the second Maxwell equation is satisfied for a " source-free " field ) and that the electromagnetic stress-energy matches the Einstein tensor.
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