Gravitational Observables and Local Symmetries

TL;DR

This paper demonstrates that in a closed universe, no gravitational observables can be constructed solely from local functions of initial data and their derivatives, based on a recent classification of local symmetries.

Contribution

It shows the impossibility of defining local gravitational observables in vacuum spacetimes using a new classification of local symmetries.

Findings

No local observables exist for vacuum gravitational fields in closed universes.

Local functions of Cauchy data cannot serve as gravitational observables.

The result relies on a recent classification of local symmetries of Einstein's equations.

Abstract

Using a recent classification of local symmetries of the vacuum Einstein equations, it is shown that there can be no observables for the vacuum gravitational field (in a closed universe) built as spatial integrals of local functions of Cauchy data and their derivatives.