Supersymmetric Dyonic Black Holes in Kaluza-Klein Theory

TL;DR

This paper explores supersymmetric dyonic black holes in Kaluza-Klein theories, revealing their geometric structure, charge configurations, and thermodynamic properties, with solutions effectively matching lower-dimensional cases.

Contribution

It provides a detailed analysis of supersymmetric dyonic black holes in higher-dimensional Kaluza-Klein theories, highlighting their geometric and thermodynamic characteristics and their relation to lower-dimensional solutions.

Findings

Solutions are effectively 4D black holes of 6D KK theory.

Null singularity with finite temperature for Q ≠ 0 and P ≠ 0.

Special cases reduce to known 5D KK black holes with naked singularities.

Abstract

We study supersymmetric, four-dimensional (4-d), Abelian charged black holes (BH's) arising in (4+n)-d (1 \le n \le 7) Kaluza-Klein (KK) theories. Such solutions, which satisfy supersymmetric Killing spinor equations (formally satisfied for any n) and saturate the corresponding Bogomol'nyi bounds, can be obtained if and only if the isometry group of the internal space is broken down to the U(1)_E \times U(1)_M gauge group; they correspond to dyonic BH's with electric Q and magnetic P charges associated with {\it different} U(1) factors. The internal metric of such configurations is diagonal with (n-2) internal radii constant, while the remaining two radii (associated with the respective electric and magnetic U(1) gauge fields) and the 4-d part of the metric turn out to be independent of n, i.e., solutions are effectively those of supersymmetric 4-d BH's of 6-d KK theory. For Q \ne 0 and P \ne 0, 4-d space-time has a null singularity, finite temperature (T_H \propto 1 / \sqrt{|QP|}) and zero entropy. Special cases with either Q=0 or P=0 correspond to the supersymmetric 4-d BH's of 5-d KK theory, first derived by Gibbons and Perry, which have a naked singularity and infinite temperature.