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

TL;DR

This paper explores static four-dimensional Abelian black holes within higher-dimensional Kaluza-Klein theory, revealing their charge configurations, thermodynamic properties, and duality symmetries.

Contribution

It provides explicit solutions for non-extreme and extreme black holes with detailed thermodynamic and charge properties, including duality transformations.

Findings

Non-extreme solutions have Schwarzschild-like spacetime, finite temperature, and entropy.

Extreme solutions are supersymmetric with null singularity, maximum temperature, and zero entropy.

Charge configurations exhibit continuous electric-magnetic duality via global SO(n) transformations.

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.