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

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.

LaTeX, 17 pages

References in corpus (1)

• The Dynamics of General Relativity

Cited by in corpus (45)

• Gravity as a field theory in flat space-time
• From the Embedding Theory to General Relativity in a result of inflation
• Embeddings for Schwarzschild metric: classification and new results
• Constraint algebra for Regge-Teitelboim formulation of gravity
• Embedding theory as new geometrical mimetic gravity
• Forms of action for perfect fluid in General Relativity and mimetic gravity
• Non-relativistic limit of embedding gravity as General Relativity with dark matter
• Hawking into Unruh mapping for embeddings of hyperbolic type
• Modifications of gravity via differential transformations of field variables
• The approach to gravity as a theory of embedded surface
• Curvature and Gravity Actions for Matrix Models II: the case of general Poisson structure
• Curvature and Gravity Actions for Matrix Models
• When does the Hawking into Unruh mapping for global embeddings work?
• New variables for the Einstein theory of gravitation
• New action for the Hilbert-Einstein equations
• Dark matter from non-relativistic embedding gravity
• Global Embedding of the Reissner-Nordström Metric in the Flat Ambient Space
• First order representation of the Faddeev formulation of gravity
• Classification of global minimal embeddings for nonrotating black holes
• Global embeddings of BTZ and Schwarzschild-AdS type black holes in a flat space
• Exact relation between canonical and metric energy-momentum tensors for higher derivative tensor field theories
• Embeddings of the black holes in a flat space
• Algebra of Implicitly Defined Constraints for Gravity as the General Form of Embedding Theory
• Dark matter as a gravitational effect in the embedding theory approach
• Classical electromagnetic potential as a part of gravitational connection: ideas and history
• Weak field limit for embedding gravity
• Gravitational energy in the framework of embedding and splitting theories
• Friedmann cosmology in Regge-Teitelboim gravity
• Ostrogradsky-Hamilton approach to geodetic brane gravity
• Lower-dimensional Regge-Teitelboim gravity
• Energy-momentum pseudotensor and superpotential for generally covariant theories of gravity of general form
• Explicit isometric embeddings of collapsing dust ball
• First order minisuperspace model for the Faddeev formulation of gravity
• Embeddings for solutions of Einstein equations
• Canonical formulation of embedding gravity in a form of General Relativity with dark matter
• Canonical description for formulation of embedding gravity as a field theory in a flat spacetime
• Possible types of dark matter condensation in embedding gravity
• Some minisuperspace model for the Faddeev formulation of gravity
• Noether and Belinfante stress-energy tensors for theories with arbitrary Lagrangians of tensor fields
• Definitions of energy for the description of gravity as the splitting theory
• Relation between quantum effects in General Relativity and embedding theory
• Investigation of Faddeev variant of embedding theory
• Discrete Faddeev action for the tetrad fields strongly varying along different coordinates
• Explicit isometric embeddings of black holes geometry with non-singular matter distribution
• Nontrivial isometric embeddings for flat spaces