Natural octonionic generalization of general relativity

TL;DR

This paper proposes a novel generalization of general relativity using complex octonions, extending the mathematical framework with new algebraic structures to explore potential physical implications.

Contribution

It introduces a complex octonionic extension of the Einstein-Hilbert action based on an achtbein formalism, linking quaternionic and octonionic algebraic structures to gravity.

Findings

Formulation of a complex octonionic gravity action

Connection between quaternionic/octonionic structures and gravity

Foundation for further exploration of octonionic gravity theories

Abstract

An intriguingly natural generalization, using complex octonions, of general relativity is pointed out. The starting point is the vierbein-based double dual formulation of the Einstein-Hilbert action. In terms of two natural structures on the (complex) quaternions and (complex) octonions, the inner product and the cross products, respectively, this action is linked with the complex quaternionic structure constants, and subsequently generalized to an achtbein-based 'double chi-dual' action in terms of the complex octonionic structure constants.