Physical quantities and spatial parameters in the complex octonion curved space

TL;DR

This paper explores how physical quantities influence the geometry of complex octonion curved space, deriving formulae that relate physical fields to spatial parameters and aligning with general relativity under weak fields.

Contribution

It introduces a novel approach using complex octonions to analyze the impact of physical quantities on curved space geometry, extending to curved function spaces.

Findings

Formulae linking physical quantities and spatial parameters

Results consistent with General Theory of Relativity in weak fields

Potential to identify physical causes of space warping

Abstract

The paper focuses on finding out several physical quantities to exert an influence on the spatial parameters of complex-octonion curved space, including the metric coefficient, connection coefficient, and curvature tensor. In the flat space described with the complex octonions, the radius vector is combined with the integrating function of field potential to become a composite radius vector. And the latter can be considered as the radius vector in a flat composite-space (a function space). Further it is able to deduce some formulae between the physical quantity and spatial parameter, in the complex-octonion curved composite-space. Under the condition of weak field approximation, these formulae infer a few results accordant with the General Theory of Relativity. The study reveals that it is capable of ascertaining which physical quantities are able to result in the warping of space, in terms of the curved composite-space described with the complex octonions. Moreover, the method may be expanded into some curved function spaces, seeking out more possible physical quantities to impact the bending degree of curved spaces.