Covariant magnetic connection hypersurfaces

In the single fluid, non-relativistic, ideal magnetohydrodynamic (MIID) plasma description, magnetic field lines play a fundamental role by defining dynamically preserved 'magnetic connections' between plasma elements. Here we show how the concept of magnetic connection needs to be generalized in the case of a relativistic MIID description where we require covariance under arbitrary Lorentz transformations. This is performed by defining 2-D magnetic connection hypersurfaces in the 4-D Minkowski space. This generalization accounts for the loss of simultaneity between spatially separated events in different frames and is expected to provide a powerful insight into the 4-D geometry of electromagnetic fields when E " B = 0.