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Phys. Rev. D 61, 024038 (1999) [18 pages]

Energy-momentum tensor for the gravitational field

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S. V. Babak*
Department of Physics and Astronomy, Cardiff University, Cardiff CF24 3YB, United Kingdom

L. P. Grishchuk
Department of Physics and Astronomy, Cardiff University, Cardiff CF24 3YB, United Kingdom
Sternberg Astronomical Institute, Moscow University, Moscow 119899, Russia

Received 7 July 1999; published 28 December 1999

The search for the gravitational energy-momentum tensor is often qualified as an attempt at 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 nonlinear 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) a 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 six 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.

© 1999 The American Physical Society

URL:
http://link.aps.org/doi/10.1103/PhysRevD.61.024038
DOI:
10.1103/PhysRevD.61.024038
PACS:
04.20.Fy, 11.10.Ef, 98.80.Hw

*Email address: babak@astro.cf.ac.uk

Email address: grishchuk@astro.cf.ac.uk