Static four-dimensional Abelian black holes in Kaluza-Klein theory

Static, four-dimensional (4D) black holes (BH’s) in (4+n)D Kaluza-Klein (KK) theory with Abelian isometry and a diagonal internal metric have at most one electric (Q) and one magnetic (P) charge, which can either come from the same U(1)-gauge field (corresponding to BH’s in effective 5D KK theory) or from different ones [corresponding to BH’s with U(1${)}_{\mathit{M}}$×U(1${)}_{\mathit{E}}$ isometry of an effective 6D KK theory]. In the later case, explicit nonextreme solutions have the global space-time of Schwarzschild BH’s, finite temperature, and nonzero entropy. In the extreme (supersymmetric) limit the singularity becomes null, the temperature saturates the upper bound ${\mathit{T}}_{\mathit{H}}$=1/(4π √‖QP‖ ), and entropy is zero. A class of KK BH’s with constrained charge configurations, exhibiting a continuous electric-magnetic duality, is generated by global SO(n) transformations on the above classes of the solutions.