Split octonion reformulation of generalized linear gravitational field equations

Abstract

In this paper, we describe the properties of split octonions and their connection with the 2 × 2 Zorn vector matrix containing both scalar and vector components. Starting with a brief description of gravito-dyons, we reformulate the generalized linear gravitational field equations of gravito-dyons in terms of split octonion. We express the generalized gravito-Heavisidian (GH) potentials, fields, and various wave equations of gravito-dyons in terms of split octonions variables. Accordingly, we demonstrate the work-energy theorem of classical mechanics reproducing the continuity equation for the case of gravito-dyons in terms of split octonions. Further, we discuss the split octonionic form of linear momentum conservation law for gravito-dyons in the case of linear gravitational theory. We have summarized the various split octonion equations for the case of the generalized GH-field of gravito-dyons and the generalized electromagnetic field of dyons. The unified fields of dyons and gravito-dyons have been demonstrated and corresponding field equations are discussed in unique and consistent manner in terms of split octonions.

Elliptic biquaternionic equations of gravitoelectromagnetism

“…13 Besides, recently, some researchers have investigated linear field equations for gravity and electromagnetic fields using Clifford algebra. [14][15][16][17][18] Elliptic biquaternions is a mathematical structure that has an algebraic structure that includes biquaternions and quaternions. It is a fact that the Proca-Maxwell equations and gravitational field equations have been studied by many researchers in the literature.…”

“…Argyris and Ciubotariu have obtained the Proca‐type gravitational field equations for electromagnetism by assuming the finite mass of graviton and adding the resulting terms 13 . Besides, recently, some researchers have investigated linear field equations for gravity and electromagnetic fields using Clifford algebra 14–18 . Elliptic biquaternions is a mathematical structure that has an algebraic structure that includes biquaternions and quaternions.…”

Horadam Octonions

“…In addition octonions are used in many subjects such as, unified fields of dyons and gravito-dyons, electrodynamic, electromagnetism . For background the reader can find their properties in [2,4,5,6,7,8].…”