Gravitational energy in the framework of embedding and splitting theories

Abstract

We study various definitions of the gravitational field energy based on the usage of isometric embeddings in the Regge-Teitelboim approach. For the embedding theory we consider the coordinate translations on the surface as well as the coordinate translations in the flat bulk. In the latter case the independent definition of gravitational energy-momentum tensor appears as a Noether current corresponding to global inner symmetry. In the field-theoretic form of this approach (splitting theory) we consider Noether procedure and the alternative method of energy-momentum tensor defining by varying the action of the theory with respect to flat bulk metric. As a result we obtain energy definition in field-theoretic form of embedding theory which, among the other features, gives a nontrivial result for the solutions of embedding theory which are also solutions of Einstein equations. The question of energy localization is also discussed.

arXiv comment19 pages. This version matches the published one. The text has been shortened and revised

References in corpus (13)

• Geodetic Brane Gravity
• Canonical formulation of the embedded theory of gravity equivalent to Einstein's General Relativity
• From the Embedding Theory to General Relativity in a result of inflation
• Gravity as a field theory in flat space-time
• Covariantized Noether identities and conservation laws for perturbations in metric theories of gravity
• Embeddings for Schwarzschild metric: classification and new results
• Constraint algebra for Regge-Teitelboim formulation of gravity
• Hawking into Unruh mapping for embeddings of hyperbolic type
• The approach to gravity as a theory of embedded surface
• External time canonical formalism for gravity in terms of embedding theory
• Algebra of Implicitly Defined Constraints for Gravity as the General Form of Embedding Theory
• Friedmann cosmology in Regge-Teitelboim gravity
• Field-Theoretical Formulation of Regge-Teitelboim Gravity

Cited by in corpus (4)

• Modifications of gravity via differential transformations of field variables
• Exact relation between canonical and metric energy-momentum tensors for higher derivative tensor field theories
• Energy-momentum pseudotensor and superpotential for generally covariant theories of gravity of general form
• Noether currents in theories with higher derivatives and theories with differential field transformation in action (DFTA)