### 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.

Original language | English |
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Article number | 1750188 |

Number of pages | 20 |

Journal | International Journal of Modern Physics D |

Volume | 27 |

Issue number | 2 |

Early online date | 5 Oct 2017 |

DOIs | |

Publication status | Published - Jan 2018 |

### Scopus subject areas

- Astronomy and Astrophysics
- Mathematical Physics
- Space and Planetary Science