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In cosmology the notion of a photon fluid is often used, i.e. a perfect fluid with the equation of state [itex]P=\frac{\rho}{3}[/itex] and the stress-energy- momentum tensor of a perfect fluid. On the other hand, a photon fluid is just an electromagnetic field with the well- known definition for its stress- energy- momentum tensor. Where is the connection between those tensors? Is the fluid's stress- energy tensor just the diagonalized version of the EM- stress- energy tensor? Or is the connection between these tensors not so obvious?

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# Energy- momentum tensor of photon fluid/EM- field

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