If the electromagnetic field $F_{ab}$ satisfies Maxwell's equations
\begin{equation*}
\nabla_{[a}F_{bc]}= 0 \quad\text{and}\quad \nabla^a F_{ab} =0
\end{equation*}
and there is a spinor $\psi$ such that
\begin{equation}\label{eq:20161115b}
(\nabla_{\mu} + i \sqrt{4 \pi} \not F \gamma_{\mu} ) \psi = 0
\end{equation}
and $i \bar \psi \gamma^{\mu} \psi$ is time-like

then the Einstein equations are satisfied as well:
\begin{equation*}
R_{\mu\nu} - \frac{1}{2} R g_{\mu\nu} = 8 \pi T_{\mu\nu}
\end{equation*}

*A*from now on) can for example be used to obtain the metric and electromagnetic field of the Israel-Wilson-Perjés (IWP) black holes. Because I wanted to generalize the IWP black holes to higher dimensions, I wanted to find the generalization of property

*A*in higher dimensions.