Canonical formulation of the embedded theory of gravity equivalent to Einstein's General Relativity

TL;DR

This paper develops a canonical formalism for an embedded gravity theory, showing its equivalence to Einstein's General Relativity through constraints and gauge fixing, providing a new perspective on gravitational dynamics.

Contribution

It introduces a canonical formulation of embedded gravity with additional constraints, establishing its equivalence to Einstein's General Relativity.

Findings

Formulation of a canonical theory with eight-parameter gauge symmetry.

Equivalence to Einstein's GR via gauge fixing or metric rewriting.

Derivation of the action for the embedded gravity theory.

Abstract

We study the approach in which independent variables describing gravity are functions of the space-time embedding into a flat space of higher dimension. We formulate a canonical formalism for such a theory in a form, which requires imposing additional constraints, which are a part of Einstein's equations. As a result, we obtain a theory with an eight-parameter gauge symmetry. This theory becomes equivalent to Einstein's general relativity either after partial gauge fixing or after rewriting the metric in the form that is invariant under the additional gauge transformations. We write the action for such a theory.