# Orthonormal Frame and SO(3) Kaluza-Klein Dyon

## TL;DR

This paper presents an alternative method using orthonormal frames and Cartan's structure equations to derive an SO(3) Kaluza-Klein dyon solution, confirming previous results obtained via Einstein's equations.

## Contribution

It introduces a new approach employing orthonormal frames and Cartan's structure equations to analyze the Kaluza-Klein dyon, validating earlier findings with a different mathematical framework.

## Key findings

- Both methods yield identical solutions.
- The orthonormal frame approach is effective for this problem.
- Results confirm the consistency of the Kaluza-Klein dyon solution.

## Abstract

In previous paper, we present an SO(3) Wu-Yang-like Kaluza-Klein dyon so- lution satisfies the Einstein equation in the seven-dimensional spacetimes. In this note, we will show an alternative approach using an orthonormal frame, the Cartan's structure equations, and calculating the affine spin connection one-form,curvature tensor and Ricci tensor. The results from these two different methods are coincident.