the four-current
Charge density tells you how much charge sits in a region; current density tells you how much charge flows. Relativity says these are not independent either — what one observer calls static charge, another moving observer sees partly as current. The four-current stitches charge density and current density into one four-vector.
The four-current is J^mu = (c rho, J_x, J_y, J_z), where rho is the charge density and J the current density; it transforms as a four-vector under Lorentz boosts. Charge conservation, which in three-dimensional form is the continuity equation d rho / d t + div J = 0, becomes the beautifully compact and manifestly invariant statement d_mu J^mu = 0 — the four-divergence of the four-current vanishes. J^mu is the source term of electromagnetism: it sits on the right-hand side of the covariant Maxwell equations, d_mu F^(mu nu) = mu_0 J^nu.
Packaging charge and current together explains a puzzle from Vol I: why a neutral current-carrying wire attracts a moving charge magnetically. In the charge's frame, a Lorentz boost of J^mu length-contracts the positive and negative charge densities differently, leaving a net charge density — the 'magnetic' force is revealed as an electrostatic one seen from another frame. The vanishing four-divergence of J^mu is also why charge conservation is not an add-on but is forced by the structure of Maxwell's equations.
A static charge distribution has J^mu = (c rho, 0, 0, 0) — all time component, no spatial current. View it from a frame moving at velocity v and the boost turns part of the time component into space components: a current J appears, exactly the convection current rho v you would expect from charge in motion.
J^mu = (c rho, J) unites charge and current; conservation is the one line d_mu J^mu = 0.
That charge is a Lorentz invariant (all observers agree on total charge) is a separate, stronger fact than J^mu being a four-vector — it is what makes charge conserved AND frame-independent. The continuity equation d_mu J^mu = 0 is automatic given the antisymmetry of F^(mu nu).