Static spin-32perturbations of a two-black-hole system

We construct the most general static regular, nongauge spin-$\frac{3}{2}$ perturbations on the Majumdar-Papapetrou background for two black holes. The construction applies a limiting procedure by combining Killing spinors and spacetime perturbations. The supercharge associated with the spin-$\frac{3}{2}$ field is proportional to the difference of the mass parameters, implying that a system of two equal black holes has zero supercharge.