Forces in the complex octonion curved space

TL;DR

This paper extends electromagnetic and gravitational field equations into complex octonion curved space, revealing how geometric properties influence physical fields and quantities.

Contribution

It introduces a framework for describing electromagnetic and gravitational fields simultaneously in complex octonion curved space, generalizing prior quaternion-based approaches.

Findings

Connection coefficients and curvature affect field strength and sources.

Geometric properties influence physical quantities like momentum and energy.

Unified description of electromagnetic and gravitational properties in complex octonion space.

Abstract

The paper aims to extend major equations in the electromagnetic and gravitational theories from the flat space into the complex octonion curved space. Maxwell applied simultaneously the quaternion analysis and vector terminology to describe the electromagnetic theory. It inspires subsequent scholars to study the electromagnetic and gravitational theories with the complex quaternions/octonions. Furthermore Einstein was the first to depict the gravitational theory by means of tensor analysis and curved four-space-time. Nowadays some scholars investigate the electromagnetic and gravitational properties making use of the complex quaternion/octonion curved space. From the orthogonality of two complex quaternions, it is possible to define the covariant derivative of the complex quaternion curved space, describing the gravitational properties in the complex quaternion curved space. Further it is possible to define the covariant derivative of the complex octonion curved space by means of the orthogonality of two complex octonions, depicting simultaneously the electromagnetic and gravitational properties in the complex octonion curved space. The result reveals that the connection coefficient and curvature of the complex octonion curved space will exert an influence on the field strength and field source of the electromagnetic and gravitational fields, impacting the linear momentum, angular momentum, torque, energy, and force and so forth.