Addendum to Supersymmetric Dyonic Black Holes in Kaluza-Klein Theory

Abstract

We complete the study of 4-dimensional (4-d), static, spherically symmetric, supersymmetric black holes (BH's) in Abelian $(4+n)$-d Kaluza-Klein theory, by showing that for such solutions $n$ electric charges $\vec{\mathcal{Q}}\equiv (Q_1,...,Q_n)$ and $n$ magnetic charges $\vec{\mathcal{P}}\equiv (P_1,...,P_n)$ are subject to the constraint $\vec{\mathcal{P}}\cdot \vec{\mathcal{Q}}=0$. 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 $U(1{)}_M\times U(1{)}_E$ BH's, {\it i.e.}, supersymmetric BH's with a diagonal internal metric.

4 pages, uses RevTex

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