Algebra of Implicitly Defined Constraints for Gravity as the General Form of Embedding Theory

Abstract

We consider the embedding theory, the approach to gravity proposed by Regge and Teitelboim, in which 4D space-time is treated as a surface in high-dimensional flat ambient space. In its general form, which does not contain artificially imposed constraints, this theory can be viewed as an extension of GR. In the present paper we study the canonical description of the embedding theory in this general form. In this case, one of the natural constraints cannot be written explicitly, in contrast to the case where additional Einsteinian constraints are imposed. Nevertheless, it is possible to calculate all Poisson brackets with this constraint. We prove that the algebra of four emerging constraints is closed, i.e., all of them are first-class constraints. The explicit form of this algebra is also obtained.

11 pages

References in corpus (4)

• Ostrogradski approach for the Regge-Teitelboim type cosmology
• Embeddings for Schwarzschild metric: classification and new results
• Hamiltonian dynamics of extended objects: Regge-Teitelboim model
• Path integrals for actions that are not quadratic in their time derivatives

Cited by in corpus (4)

• Modifications of gravity via differential transformations of field variables
• Dark matter as a gravitational effect in the embedding theory approach
• Gravitational energy in the framework of embedding and splitting theories
• Canonical description for formulation of embedding gravity as a field theory in a flat spacetime