The Rotating Dyonic Black Holes Of Kaluza-Klein Theory

TL;DR

This paper presents explicit solutions for rotating dyonic black holes in five-dimensional Kaluza-Klein theory, revealing novel properties such as arbitrarily large gyromagnetic ratios and unique extremal solution behaviors.

Contribution

It provides the most general explicit form of rotating dyonic black holes in 5D Kaluza-Klein theory, including thermodynamic and stability analyses, and uncovers surprising physical properties.

Findings

Gyromagnetic and gyroelectric ratios can be arbitrarily large.

Extreme solutions can have zero angular velocity with non-zero angular momentum.

Certain extreme solutions allow adding angular momentum without changing mass or charges.

Abstract

The most general electrically and magnetically charged rotating black hole solutions of 5 dimensional \KK\ theory are given in an explicit form. Various classical quantities associated with the black holes are derived. In particular, one finds the very surprising result that the gyromagnetic and gyroelectric ratios can become {\tenit arbitrarily large}. The thermodynamic quantities of the black holes are calculated and a Smarr-type formula is obtained leading to a generalized first law of black hole thermodynamics. The properties of the extreme solutions are investigated and it is shown how they naturally separate into two classes. The extreme solutions in one class are found to have two unusual properties: (i). Their event horizons have zero angular velocity and yet they have non-zero ADM angular momentum. (ii). In certain circumstances it is possible to add angular momentum to these extreme solutions without changing the mass or charges and yet still maintain an extreme solution. Regarding the extreme black holes as elementary particles, their stability is discussed and it is found that they are stable provided they have sufficient angular momentum.