Modified Einstein equations

TL;DR

This paper proposes a modification to Einstein's equations by including a compensating tensor field to account for coordinate changes during metric variation, addressing a limitation in the standard variational approach.

Contribution

It introduces a new tensor field and modifies the variational principle to incorporate coordinate changes in deriving Einstein equations.

Findings

Modified Einstein equations with additional tensor field

Addresses coordinate variation effects in the variational principle

Potential implications for gravitational theory consistency

Abstract

Standard general relativity fails to take into account the changes in coordinates induced by the variation of metric in the Hilbert action principle. We propose to include such changes by introducing a fundamental compensating tensor field and modifying the usual variational procedure.