Nov
09

New equations for gravitation with the Riemann tensor and 4-index energy-momentum tensors for gravitation and matter [1]

      Zahid Zakir [2]

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, v1,   9 November 2010

Online: TPAC: 3600-017 v2, 28 September 2012; DOI:  10.9751/TPAC.3600-017


[1] The preprint of the paper has been presented in 1999 (revised 2003): Zakir Z. arXiv:gr-qc/9905009

[2] Centre for Theoretical Physics and Astrophyics, Tashkent, Uzbekistan

      zahidzakir@theor-phys.org


3 Responses to “TPAC: 3600-017 v2, Vol. 5, p. 14–17”

  1. Zahid Zakir
    October 9th, 2012 at 04:03 | #1

    1. New result:
    A generalized version of the Einstein equations in the 4-index form, containing the Riemann curvature tensor linearly, is derived.

  2. Zahid Zakir
    October 9th, 2012 at 04:04 | #2

    2. New result:
    It is shown, that the gravitational energy-momentum density outside a source is represented across the Weyl tensor vanishing at the 2-index contraction.

  3. Zahid Zakir
    October 9th, 2012 at 04:06 | #3

    3. New result:
    The 4-index energy-momentum density tensor for matter also is constructed.

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