Addendum to supersymmetric dyonic black holes in Kaluza-Klein theory

We complete the study of 4-dimensional (4-d), static, spherically symmetric, supersymmetric black holes (BHʹs) in Abelian (4+n)-d Kaluza-Klein theory, by showing that for such solutions n electric charges Q ≡ (Qi,…,Qn) and n magnetic charges P ≡ (P1,…,Pn) are subject to the constraint P · Q = 0. All such solutions can be obtained by performing the SO(n) rotations, which do not affect the 4-d space-time metric and the volume of the internal space, on the supersymmetric U(1)M × U(1)E BHʹs, i.e., supersymmetric BHʹs with a diagonal internal metric.