 Einstein-Maxwell theory

The Einstein-Maxwell system couples the metric to an electromagnetic field. In geometrized units its source-free equations are $G_{ab}=8\pi T_{ab}^{\mathrm{EM}}$, ${\nabla }_a{F}^{ab}=0$ and $dF=0$, with $T_{ab}^{\mathrm{EM}}=(F_{ac}{F}_b{}^c-\frac{1}{4}{g}_{ab}{F}_{cd}{F}^{cd})/(4\pi )$. Electrovacuum need not have vanishing Ricci tensor, so a Komar integral need not be unchanged between different enclosing surfaces.