section we are going to study the consequences of demanding the black-hole solutions of $N=2,d=4$ supergravity to be everywhere supersymmetric.

The KSIs of $N=2,d=4$ supergravity are given in Eqs. (\[eq:ksipsi\]) and (\[eq:ksilambda\]) and they lead to Eqs. (\[eq:ksi1\])-(\[eq:ksi2-1\]) for configurations in the timelike class. Since we are going to consider configurations that solve the equations of motion, it may seem that the KSIs are automatically satisfied. However, most solutions have singularities at which the equations of motion are not satisfied, i.e. one has $\mathcal{E}(\phi)=\mathcal{J}(\phi)$. The r.h.s. of the equations of motion at the singularities can be associated to sources for the corresponding fields and the KSIs are then understood as relations between the possible sources of supersymmetric solutions: the KSIs put constraints on possible sources of supersymmetric solutions.

Let us consider from this point of view the KSIs Eqs. (\[eq:ksi1\])-(\[eq:ksi2-1\]): the first of them, Eq. (\[eq:ksi1\]), tells us that the components $\mathcal{E}^{0m}$ and $\mathcal{E}^{mn}$ of the Einstein equations must vanish automatically for supersymmetric configurations and they must do so everywhere if the solutions are everywhere supersymmetric. This means that the sources $\mathcal{J}^{0m}$ and $\mathcal{J}^{mn}$ of the Einstein equation must vanish identically everywhere

$$\label{eq:J0mJmn}
\mathcal{J}^{0m}=\mathcal{J}^{mn}=0\, .$$

Hence, singular (delta-like) sources are 