Einstein-Maxwell theory
= Einstein-Maxwell theory
{c}
The Einstein-Maxwell system couples the metric to an electromagnetic field. In geometrized units its source-free equations are $G_{ab}=8\pi T_{ab}^{\mathrm{EM}}$, $\nabla_aF^{ab}=0$ and $dF=0$, with $T_{ab}^{\mathrm{EM}}=(F_{ac}F_b{}^c-\tfrac14g_{ab}F_{cd}F^{cd})/(4\pi)$. Electrovacuum need not have vanishing Ricci tensor, so a Komar integral need not be unchanged between different enclosing surfaces.