In special and general relativity, the four-current is the Lorentz covariant four-vector that replaces the electromagnetic current density

where c is the speed of light, ρ the charge density , and j the conventional current density.

In special relativity, the statement of charge conservation (sometimes also called the contnuity equation) is that the Lorentz invariant divergence of J is zero:

where D is an operator called the four-gradient and given by (1/c ∂/∂t, -∇). Sometimes, the above relation is written as

J^a_,a = 0

In general relativity, the continuity equation is written as:

J^a_;a = 0

where the semi-colon represents a covariant derivative.