A systematic development of the photon 4-momentum in the non-quantic perspective of General Relativity is very difficult to find in the scientific litterature. However, the photon 4-momentum is a fundamental concept if one wants to study relativistic transport theory or Compton collision formulae. For these reasons, a coherent formalism has been elaborated. It sysmetically allows one to formulate these problems the criterion of validity being the fact that in the case of the Minkowski metric, the general formulae give the classical results of the Special Relativity.