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TPAC: 3600-017, Vol. 5, No 2, p. 14–17

9 November 2010 · Zahid Zakir

New equations for gravitation with the Riemann tensor and 4-index energy-momentum tensors for gravitation and matter

Zahid Zakir

Abstract

A generalized version of the Einstein equations in the 4-index form, containing the Riemann curvature tensor linearly, is derived. It is shown, that the gravitational energy-momentum density outside a source is represented across the Weyl tensor vanishing at the 2-index contraction. The 4-index energy-momentum density tensor for matter also is constructed.

PACS: 04.20.Cv, 04.20.Fy, 11.10.-z

Key words: gravitational energy, curvature tensor, vacuum energy

Vol. 5, No 2, p. 14–17, 9 November 2010.

DOI: 10.9751/TPAC.3600-017

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The source notes an earlier preprint: arXiv:gr-qc/9905009 (1999, revised 2003).