= Solution
In an orthonormal frame, $F_{0i}=-E_i$ and $F_{ij}=\epsilon_{ijk}B_k$. The <electromagnetic stress-energy tensor> gives
$$
T_{00}=\frac{E^2+B^2}{8\pi},\qquad T_{0i}=-\frac{(\mathbf E\times\mathbf B)_i}{4\pi}.
$$
The sign of $T_{0i}$ follows directly from $F_{0j}F_i{}^j=-E_j\epsilon_{ijk}B_k$. Thus
$$
T_{00}^2-\sum_iT_{0i}^2
=\frac{(E^2-B^2)^2+4(\mathbf E\cdot\mathbf B)^2}{64\pi^2}\ge0,
$$
and $T_{00}\ge0$. These formulas hold in every local <Lorentz frame>, so the criterion just proved establishes the <dominant energy condition>. Equality occurs for a nonzero null <Maxwell field> with $E^2=B^2$ and $\mathbf E\cdot\mathbf B=0$, whose energy current is <null vector>.
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