Energy Momentum Tensor

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Energy Momentum Tensor

:

T^{\alpha\beta} = rac{1}{4\pi} -F^{\alpha \gamma}F_{\gamma}^{\beta}+rac{1}{4}g^{\alpha\beta}F_{\gamma\delta}F^{\gamma\delta}

.
And in explicit matrix form:
:

T^{\alpha\beta} =\begin{bmatrix} rac{E^2+B^2}{8\pi} & rac{S_x}{c} & rac{S_y}{c} & rac{S_z}{c} \ rac{S_x}{c} & -\sigma_{xx} & -\sigma_{xy} & -\sigma_{xz} \
rac{S_y}{c} & -\sigma_{yx} & -\sigma_{yy} & -\sigma_{yz} \
rac{S_z}{c} & -\sigma_{zx} & -\sigma_{zy} & -\sigma_{zz} \end{bmatrix}

where
:

\overrightarrow{S}=rac{c}{4\pi}\overrightarrow{E}	imes\overrightarrow{H}

is Poynting Vector ,
:

F_{\alpha\beta}

is the Electromagnetic Field Tensor ,
:

g_{\alpha\beta}

is the metric tensor and
:

\sigma_{\alpha\beta}

is Maxwell Stress Tensor