Nonabelian Kaluza-Klein Dyon

TL;DR

This paper introduces a novel nonabelian Kaluza-Klein dyon solution in seven-dimensional spacetime, featuring a spherically symmetric metric that satisfies Einstein's equations and incorporates a Schwarzschild black hole in four dimensions.

Contribution

It presents a new Wu-Yang-like Kaluza-Klein dyon solution with a spherically symmetric metric and automatic derivation of the Yang-Mills stress-energy tensor from Einstein's equations.

Findings

The solution satisfies Einstein's equations in seven dimensions.

The Ricci scalar curvature of the spacetime vanishes.

The four-dimensional part of the metric is the Schwarzschild black hole.

Abstract

We propose a new nonabelian Kaluza-Klein dyon solution in the seven-dimensional spacetimes. This is a Wu-Yang-like Kaluza-Klein dyon. The dyonic metric is spherically symmetric, two spherical coordinate systems are used, and the metric admits SO(3) Killing vectors. It can be verified that the Einstein equation is satisfied in seven-dimensional spacetimes. The stress-energy tensor of the Yang-Mills field in Einstein equation is derived from Ricci tensor automatically, not put by hand from outside. The Ricci scalar curvature \bar{R} vanishes. The four-dimensional part of the dyonic metric is just the Schwarzschild black hole metric.