English

The Energy-Momentum Tensor for the Gravitational Field

General Relativity and Quantum Cosmology 2009-10-31 v2 Astrophysics High Energy Physics - Theory

Abstract

The search for the gravitational energy-momentum tensor is often qualified as an attempt of looking for ``the right answer to the wrong question''. This position does not seem convincing to us. We think that we have found the right answer to the properly formulated question. We have further developed the field theoretical formulation of the general relativity which treats gravity as a non-linear tensor field in flat space-time. The Minkowski metric is a reflection of experimental facts, not a possible choice of the artificial ``prior geometry''. In this approach, we have arrived at the gravitational energy-momentum tensor which is: 1) derivable from the Lagrangian in a regular prescribed way, 2) tensor under arbitrary coordinate transformations, 3) symmetric in its components, 4) conserved due to the equations of motion derived from the same Lagrangian, 5) free of the second (highest) derivatives of the field variables, and 6) is unique up to trivial modifications not containing the field variables. There is nothing else, in addition to these 6 conditions, that one could demand from an energy-momentum object, acceptable both on physical and mathematical grounds. The derived gravitational energy-momentum tensor should be useful in practical applications.

Keywords

Cite

@article{arxiv.gr-qc/9907027,
  title  = {The Energy-Momentum Tensor for the Gravitational Field},
  author = {S V Babak and L P Grishchuk},
  journal= {arXiv preprint arXiv:gr-qc/9907027},
  year   = {2009}
}

Comments

32 pages, revised version, additional references, to be published in Phys. Rev. D