Original: Covariant formulation of Maxwell's equations In special relativity, in order to more clearly express the fact that Maxwell's equations in vacuum take the same form in any inertial coordinate system, Maxwell's equations are written in terms of four-vectors and tensors in the "manifestly covariant" form.
Simplified: In special relativity, Maxwell's equations for the vacuum are written in terms of four-vectors and tensors in the "manifestly covariant" form. This has been done to show more clearly the fact that Maxwell's equations (in vacuum) take the same form in any inertial coordinate system.