All the Four-Dimensional Static, Spherically Symmetric Solutions of Abelian Kaluza-Klein Theory

We present the explicit form for all the four-dimensional, static, spherically symmetric solutions in ($4+n$)-d Abelian Kaluza-Klein theory by performing a subset of $\mathrm{SO}(2, n)$ transformations corresponding to four SO(1, 1) boosts on the Schwarzschild solution, supplemented by $\frac{\mathrm{SO}\mathrm{}\left(n\right)\mathrm{}}{\mathrm{SO}\mathrm{}(n-2\mathrm{})\mathrm{}}$ transformations. The solutions are parametrized by the mass $M$, Taub-NUT charge $a$, and $n$ electric $\overrightarrow{\mathcal{Q}}$ and $n$ magnetic $\overrightarrow{\mathcal{P}}$ charges. Nonextreme black holes (with zero Taub-NUT charge) have either the Reissner-Nordström or Schwarzschild global space-time. Supersymmetric extreme black holes have a null or naked singularity, while nonsupersymmetric extreme ones have a global space-time of extreme Reissner-Nordström black holes.