Search for a "Gravitoid" Theory

TL;DR

This paper proposes a novel gravitational framework called gravitoid theory, linking matroid theory with M-theory, and explores connections between matroids and supergravity symmetries.

Contribution

It introduces gravitoid theory by integrating matroid concepts with graviton models and M-theory, highlighting new mathematical links to supergravity.

Findings

Identifies a connection between the Fano matroid and D=11 supergravity.

Links affine matroid AG(3,2) with G2-symmetry in supergravity.

Proposes a mathematical structure unifying graviton and matroid theories.

Abstract

By combining the concepts of graviton and matroid, we outline a new gravitational theory which we call gravitoid theory. The idea of this theory emerged as an attempt to link the mathematical structure of matroid theory with M-theory. Our observations are essentially based on the formulation of matroid bundle due to MacPherson and Anderson-Davis. Also, by considering the oriented matroid theory, we add new observations about the link between the Fano matroid and D=11 supergravity which was discussed in some of our recent papers. In particular we find a connection between the affine matroid AG(3,2) and the $G_ {2}-$symmetry of D=11 supergravity.