STATIC FOUR-DIMENSIONAL ABELIAN BLACK HOLES IN KALUZA-KLEIN THEORY

Abstract

Static, four-dimensional (4-d) black holes (BH's) in ($4+n$)-d Kaluza-Klein (KK) theory with Abelian isometry and diagonal internal metric have at most one electric ($Q$) and one magnetic ($P$) charges, which can either come from the same $U(1)$-gauge field (corresponding to BH's in effective 5-d KK theory) or from different ones (corresponding to BH's with $U(1{)}_M\times U(1{)}_E$ isometry of an effective 6-d KK theory). In the latter case, explicit non-extreme solutions have the global space-time of Schwarzschild BH's, finite temperature, and non-zero entropy. In the extreme (supersymmetric) limit the singularity becomes null, the temperature saturates the upper bound $T_H=1/4\pi \sqrt{|QP|}$, and entropy is zero. A class of KK BH's with constrained charge configurations, exhibiting a continuous electric-magnetic duality, are generated by global $SO(n)$ transformations on the above classes of the solutions.

11 pages, 2 Postscript figures. uses RevTeX and psfig.sty (for figs) paper and figs also at ftp://dept.physics.upenn.edu/pub/Cvetic/UPR-645-T

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