Electromagnetic stress-energy tensor
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In physics, the electromagnetic stress-energy tensor is the portion of the stress-energy tensor due to the electromagnetic field. In free space, it is given by (in cgs units):
![T^{\alpha\beta} = \frac{1}{4\pi} [ -F^{\alpha \gamma}F_{\gamma}^{\beta}+\frac{1}{4}g^{\alpha\beta}F_{\gamma\delta}F^{\gamma\delta}]](../../../math/c/8/7/c87b19ea18adaa5ba58a9514904299e7.png)
.
And in explicit matrix form:
where
is Poynting vector,
is the Electromagnetic field tensor,
is the metric tensor and
is Maxwell stress tensor
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, 
, of the energy momentum tensor represents the flux of the αth-component of the four-momentum of the electromagnetic field, 
, going through a hyperplane xβ = constant. It represents the contribution of electromagnetism to the source of the gravitational field (curvature of space-time) in general relativity.
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