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In relativistic physics, the electromagnetic stress–energy tensor is the contribution to the stress–energy tensor due to the electromagnetic field. The stress–energy tensor describes the flow of energy and momentum in spacetime. The electromagnetic stress–energy tensor contains the classical Maxwell stress tensor that governs the electromagnetic interactions.
Contents
SI units
In free space and flat space–time, the electromagnetic stress–energy tensor in SI units is
where
Explicitly in matrix form:
where
is the Poynting vector,
is the Maxwell stress tensor, and c is the speed of light. Thus,
CGS units
The permittivity of free space and permeability of free space in cgs-Gaussian units are
then:
and in explicit matrix form:
where Poynting vector becomes:
The stress–energy tensor for an electromagnetic field in a dielectric medium is less well understood and is the subject of the unresolved Abraham–Minkowski controversy.
The element
Algebraic properties
The electromagnetic stress–energy tensor has several algebraic properties:
The symmetry of the tensor is as for a general stress–energy tensor in general relativity. The tracelessness relates to the masslessness of the photon.
Conservation laws
The electromagnetic stress–energy tensor allows a compact way of writing the conservation laws of linear momentum and energy in electromagnetism. The divergence of the stress–energy tensor is:
where
This equation is equivalent to the following 4D conservation laws
respectively describing the flux of electromagnetic energy density
and electromagnetic momentum density
where J is the electric current density and ρ the electric charge density.