Consistent Hamiltonian Reduction

TL;DR

This paper demonstrates that a recent (2+2) Hamiltonian reduction of Einstein's equations maintains general covariance, with consistency shown through equivalence to Ricci-flat conditions in specific coordinates.

Contribution

It provides a proof of consistency for the (2+2) Hamiltonian reduction, ensuring it aligns with the principles of general covariance in general relativity.

Findings

Hamiltonian equations match Ricci-flat conditions

Reduction preserves general covariance

Proof of consistency is extrinsic

Abstract

I show that the recently proposed (2+2) Hamiltonian reduction of Einstein's equations of 4-dimensional spacetimes is consistent with general covariance. The consistency proof is {\it extrinsic}, as it follows from the fact that Hamilton's equations derived from the non-zero gravitational Hamiltonian are identical to the Ricci-flat condition of 4-dimensional spacetimes in privileged coordinates.