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.

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

References in corpus (2)

• Embeddings for Schwarzschild metric: classification and new results
• Algebra of Implicitly Defined Constraints for Gravity as the General Form of Embedding Theory

Cited by in corpus (1)

• Modifications of gravity via differential transformations of field variables