Addendum: Observables for General Relativity related to geometry

TL;DR

This addendum simplifies the algebra of observables in General Relativity, enabling a canonical subalgebra and a natural phase space reduction, thus clarifying and strengthening previous results.

Contribution

It demonstrates a simplification of the observable algebra in General Relativity, facilitating phase space reduction and clarifying earlier findings.

Findings

The algebra of observables is simpler than previously described.

A canonical subalgebra is identified, enabling phase space reduction.

The results strengthen the understanding of observable structures in General Relativity.

Abstract

In this addendum we clarify a point which strengthens one of the results from [the original paper]. Namely, we show that the algebra of the observables $F(r,\theta)$ is yet simpler then it was described in [the original paper]. This is an important point, because with this simplification an important subalgebra becomes canonical, allowing for a natural reduction of the phase space.