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Gravitational energy in Van Stockum space-time

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Abstract

The purpose of this paper is to illustrate the problem of energy and momentum distributions of Van Stockum space-time within the framework of two different theories of gravity, general relativity and teleparallel gravity. We have shown that for all homogeneous space-times with metric components \(g_{\mu \nu }\) being functions of time variable, t, alone and independent of space variables the total gravitational energy for any finite volume is identically zero. By working with general relativity, we have calculated the energy-momentum density for Van Stockum space-time using double index complexes and in the framework teleparallel gravity, we used the energy-momentum complexes of Einstein, Bergmann–Thomson and Landau–Lifshitz. In our analysis, we sustained that general relativity and teleparallel gravity are equivalent theories of space-time under consideration. For space-time under consideration, we have shown that different complexes of energy-momentum density do not provide the same results neither in general relativity nor in teleparallel gravity.

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Notes

  1. \({\tilde{\Gamma }}^{\rho }_{ \mu \nu } =\frac{1}{2}g^{\rho \sigma }(g_{\mu \sigma ,\nu }+g_{\nu \sigma ,\mu } -g_{\mu \nu ,\sigma })\)

  2. Finding energy-momentum density using Møller prescription in the theory of teleparallel gravity will be postponed to another article.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, University of Jeddah, Jeddah, 21589, Saudi Arabia

    Ragab M. Gad & H. A. Alharbi

  2. Department of Mathematics, Faculty of Science, Minia University, El-Minia, 61915, Egypt

    Ragab M. Gad

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  1. Ragab M. Gad
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  2. H. A. Alharbi
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Correspondence to Ragab M. Gad.

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Gad, R.M., Alharbi, H.A. Gravitational energy in Van Stockum space-time. Indian J Phys 96, 1591–1597 (2022). https://doi.org/10.1007/s12648-021-02085-2

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