Constraint algebra for Regge-Teitelboim formulation of gravity

TL;DR

This paper develops a canonical formalism for the Regge-Teitelboim gravity model, deriving its constraint algebra and relating it to the ADM formalism of Einstein's gravity.

Contribution

It provides the exact form of the first-class constraint algebra for the Regge-Teitelboim gravity formulation, highlighting its relation to ADM constraints.

Findings

Constraint algebra contains four constraints forming a subalgebra.

When these constraints are satisfied, the algebra matches ADM gravity.

Additional first-class constraints are identified and discussed.

Abstract

We consider the formulation of the gravity theory first suggested by Regge and Teitelboim where the space-time is a four-dimensional surface in a flat ten-dimensional space. We investigate a canonical formalism for this theory following the approach suggested by Regge and Teitelboim. Under constructing the canonical formalism we impose additional constraints agreed with the equations of motion. We obtain the exact form of the first-class constraint algebra. We show that this algebra contains four constraints which form a subalgebra (the ideal), and if these constraints are fulfilled, the algebra becomes the constraint algebra of the Arnowitt-Deser-Misner formalism of Einstein's gravity. The reasons for the existence of additional first-class constraints in the canonical formalism are discussed.