supergravity will indeed be the Majumdar-Papapetrou solutions. We will have to consider more general $N=2,d=4$ theories in order to be able to have stationary solutions such as the one found in Ref. [@Elvang:2005sa], that satisfy the KSIs and have positive mass. This will be done in Section \[sec-generaln2d4\].

Next, let us consider the KSI Eq. (\[eq:ksi3\]) which relates the sources of the scalar fields with those of the vector fields. If we consider only point-like sources and call $\Sigma_{A}$ the scalar charge at $\vec{x}_{A}$, this equation implies, at each sources

$$\Sigma_{A}=2e^{-i\alpha}\left.\mathfrak{D}_{i}\mathcal{Z}\right|_{\vec{x}_{A}}\, .$$

As mentioned before, the scalar sources are completely determined by the electric and magnetic charges and the asymptotic values of the scalar fields. This is known as *secondary scalar hair* [@Coleman:1991ku]. Primary scalar hair correspond to completely free parameters as in the Einstein-scalar solutions of Ref. [@kn:JNW] or in the solutions of Ref. [@Agnese:1994zx] which may be embedded in $N=4,d=4$ supergravity. Neither of these solutions is supersymmetric (nor regular) and the above KSI explains just why.

But there is more to the above KSI: it shows that the existence of attractors at the sources implies total absence of scalar sources, either of primary or secondary type. Since this 