Hamiltonian dynamics for Einstein's action in G$\rightarrow$0 limit

TL;DR

This paper performs a Hamiltonian analysis of Einstein's action in the G→0 limit, revealing it has no physical degrees of freedom and identifying its symmetries, while also developing a covariant canonical formalism.

Contribution

It introduces a Hamiltonian and covariant formalism for Einstein's action in the G→0 limit, highlighting its gauge symmetries and absence of physical degrees of freedom.

Findings

The G→0 limit of Einstein's action has no physical degrees of freedom.

The relevant symmetries and gauge transformations are explicitly identified.

A gauge-invariant symplectic form is constructed in the covariant formalism.

Abstract

The Hamiltonian analysis for the Einstein's action in $ G\to 0 $ limit is performed. Considering the original configuration space without involve the usual $ADM$ variables we show that the version $ Gto 0 $ for Einstein's action is devoid of physical degrees of freedom. In addition, we will identify the relevant symmetries of the theory such as the extended action, the extended Hamiltonian, the gauge transformations and the algebra of the constraints. As complement part of this work, we develop the covariant canonical formalism where will be constructed a closed and gauge invariant symplectic form. In particular, using the geometric form we will obtain by means of other way the same symmetries that we found using the Hamiltonian analysis.