 Mixed electromagnetic energy-flux signs

With $(+---)$ signature and $c=1$, $T^0{}_0=(E^2+B^2)/(2{\mu }_0)$ while $T^0{}_i=-(\mathbf{E}\times \mathbf{B}{)}_i/{\mu }_0$. Raising the second index gives $T^{0i}=S_i$, where $\mathbf{S}$ is the Poynting vector, and symmetry gives the physical energy-flux components $T^{i0}$. The negative mixed component is a metric-sign effect, not reversed energy transport. In SI coordinates $x^0=ct$, $T^{i0}=S_i/c$.