On a certain formulation of the Einstein equations

TL;DR

This paper introduces a specific differential system on R^6 that locally characterizes Lorentzian 4-manifolds satisfying Einstein's equations, establishing a new formulation with potential implications for understanding solutions.

Contribution

It presents a novel differential system formulation of Einstein equations on R^6, linking geometric structures to solutions of Einstein's equations.

Findings

Defines a differential system on R^6 related to Einstein manifolds

Shows the system locally characterizes Lorentzian 4-manifolds satisfying Einstein equations

Indicates a converse relationship, to be detailed in future work

Abstract

We define a certain differential system on an open set of $R^6$. The system locally defines a Lorentzian 4-manifold satisfying the Einstein equations. The converse statement is indicated and its details are postponed to the furthcoming paper.