Gravitini zero modes riding on top of multiple black holes

We study gravitini zero modes in four dimensional $\mathcal{N}=2$ pure supergravity theory. The we are solutions to the Rarita-Schwinger equations of motion background purely bosonic Majumdar-Papapetrou background. start with a very generic ansatz for that involves 32 functions and reduce set linear coupled partial differential on ${\mathbf{R}}^{3}$: kind familiar from electromagnetism divergences, curls, etc. first show how due broken supersymmetries arise this setup they solve ${\mathbf{R}}^{3}$. Then go obtain other these equations: ``extra'' fermion modes, parametrized by integration constants (one corresponds supersymmetries). A careful analysis gauge reveals have independent extra modes.