Classical Geometrodynamics with Zorn Vector-Matrix Algebra for Gravito-Dyons

Abstract

Describing the properties of split octonions and their connection with the 2 × 2 Zorn vector-matrix, we have reformulated generalized linear gravitational field equations in terms of split octonions in consistent and symmetrical manner. Starting with 2 × 2 Zorn vector-matrix algebra, we have written the generalized gravito-Heavisidian (GH) potential, field and current equations of gravito-dyons in terms of split octonions. Accordingly, we have obtained the gravitational analogues of generalized Dirac–Maxwell's and Proca–Maxwell's equations for linear gravito-Heavisidian (GH) field of gravito-dyons in the case of split octonionic representation. We have made an attempt to write the Poynting theorem in terms of split octonions which is analogous to the work-energy theorem of classical mechanics reproducing the continuity equation. Accordingly, we have described some fundamental laws of physics, i.e. the conservation of energy and momentum for the case of classical geometro-dynamics which exhibits linear gravitational theory of gravito-dyons.