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

Understand

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.