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 SO(2, n) transformations corresponding to four SO(1, 1) boosts on the Schwarzschild solution, supplemented by SO(n)/SO(n-2) transformations. The solutions are parametrized by the mass M, Taub-NUT charge a, and n electric Q⃗ and n magnetic P⃗ 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.