Charged Rotating Kaluza-Klein Black Holes in Dilaton Gravity

TL;DR

This paper constructs a new class of slowly rotating charged Kaluza-Klein black hole solutions in five-dimensional Einstein-Maxwell-dilaton theory, analyzing how the dilaton field influences their physical properties and gyromagnetic ratio.

Contribution

It introduces a novel family of black hole solutions with arbitrary dilaton coupling, extending previous models and exploring the impact of the dilaton on black hole characteristics.

Findings

The dilaton field modifies the gyromagnetic ratio.

The gyromagnetic ratio decreases as the dilaton coupling increases.

Solutions reduce to known five-dimensional black holes when the squashing function is absent.

Abstract

We obtain a class of slowly rotating charged Kaluza-Klein black hole solutions of the five-dimensional Einstein-Maxwell-dilaton theory with arbitrary dilaton coupling constant. At infinity, the spacetime is effectively four-dimensional. In the absence of the squashing function, our solution reduces to the five-dimensional asymptotically flat slowly rotating charged dilaton black hole solution with two equal angular momenta. We calculate the mass, the angular momentum and the gyromagnetic ratio of these rotating Kaluza-Klein dilaton black holes. It is shown that the dilaton field and the non-trivial asymptotic structure of the solutions modify the gyromagnetic ratio of the black holes. We also find that the gyromagnetic ratio crucially depends on the dilaton coupling constant, \alpha, and decreases with increasing \alpha for any size of the compact extra dimension.