ALL THE 4-DIMENSIONAL STATIC, SPHERICALLY SYMMETRICAL 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 (Q) over right arrow and n magnetic (P) over right arrow charges. Nonextreme black holes (with zero Taub-NUT charge) have either the Reissner-Nordstrom 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-Nordstrom black holes.