In special and General_relativity, the '''four-current''' is the Lorentz_covariant Four-vector that replaces the Electromagnetic Current_density, or indeed any conventional current density.
:
where
:''c'' is the Speed_of_light
:ρ the Charge_density
:'''j''' the conventional Current_density.
In special relativity, the statement of charge conservation (also called the Continuity_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
In general relativity, the continuity equation is written as:
where the semi-colon represents a Covariant_derivative.
See also Noether's_theorem.
Category:Electromagnetism
Category:Minkowski_spacetime
Category:Relativity
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