Archive

Archive for the ‘5. Cosmology’ Category

Nov
09

Four-index energy-momentum tensors for gravitation and matter [1]

      Zahid Zakir [2]

Abstract

   The 4-index energy-momentum tensors for gravitation and matter are analyzed on the basis of new equations for the gravitational field with the Riemann tensor. Some properties of such defined gravitational energy are discussed.

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

Key words: gravitational energy, curvature tensor, vacuum energy

Vol. 5, No 2, p. 18 – 21, v1,   9 November 2010

Online: TPAC: 3600-018 v2,  28 September 2012; DOI: 10.9751/TPAC.3600-018


[1] The preprint of the paper has been presented in 1999 (revised 2003): Zakir Z. arXiv:gr-qc/9905036

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

      zahidzakir@theor-phys.org


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