TL;DR
This paper proves the involutivity of key field equations like Einstein and Einstein-Maxwell by calculating Spencer cohomology, linking it with Cartan's method, and exploring implications via Cartan-Kahler theory.
Contribution
It introduces a cohomological approach to establish the involutivity of fundamental field equations, connecting Spencer cohomology with Cartan's method.
Findings
Proves involutivity of Einstein and Einstein-Maxwell equations.
Establishes a detailed relation between Spencer cohomology and Cartan's method.
Derives implications for the structure of field equations using Cartan-Kahler theory.
Abstract
We prove involutivity of Einstein, Einstein-Maxwell and other field equations by calculating the Spencer cohomology of these systems. Relation with Cartan method is traced in details. Basic implications through Cartan-Kahler theory are derived.
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