Spacetime deployments parametrized by gravitational and electromagnetic fields

TL;DR

This paper develops a mathematical framework linking electromagnetic and gravitational fields to spacetime deformations using conformally invariant properties and PDE theory, applicable across various spacetime dimensions.

Contribution

It introduces a novel parametrization of spacetime deployments based on gauge fields derived from conformally invariant properties, extending to higher dimensions.

Findings

Explicit dependence of spacetime functions on n(n+1) parameters

Unified description of electromagnetic and gravitational fields

Applicability to spacetime dimensions n ≥ 4

Abstract

On the basis of a "Punctual" Equivalence Principle of the general relativity context, we consider spacetimes with measurements of conformally invariant physical properties. Then, applying the Pfaff theory for PDE to a particular conformally equivariant system of differential equations, we make explicit the dependence of any kind of function describing a "spacetime deployment", on n(n+1) parametrizing functions, denoting by n the spacetime dimension. These functions, appearing in a linear differential Spencer sequence and determining gauge fields of spacetime deformations relatively to a "substrat spacetime", can be consistently ascribed to unified electromagnetic and gravitational fields, at any spacetime dimensions n greater or equal to 4.