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arXiv · 1802.00738

$4$-index theory of gravity and its relation with the violation of the energy-momentum conservation law

H. Moradpour·I. Licata·C. Corda·Ines G. Salako
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Abstract

Recently, a $4$-index generalization of the Einstein theory is proposed by Moulin (Eur. Phys. J. C 77, 878 (2017)). Using this method, we find the most general $2$-index field equations derivable from the Einstein-Hilbert action. The application of Newtonian limit, the role of gravitational coupling constant and the effects of the properties of ordinary energy-momentum tensor in obtaining a $4$-index gravity theory have been studied. We also address the results of building Weyl free $4$-index gravity theory. Our study displays that both the Einstein and Rastall theories can be obtained as the subclasses of a $4$-index gravity theory which shows the power of $4$-index method in unifying various gravitational theories. It is also obtained that the violation of the energy-momentum conservation law may be allowed in $4$-index gravity theory, and moreover, the contraction of $4$-index theory generally admits a non-minimal coupling between geometry and matter field in the Rastall way. This study also shows that, unlike the Einstein case, the gravitational coupling constant of $4$-index Rastall theory generally differs from that of the ordinary $2$-index Rastall theory.

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H. Moradpour, I. Licata, C. Corda, Ines G. Salako. 2018-01-29. $4$-index theory of gravity and its relation with the violation of the energy-momentum conservation law. https://doi.org/10.1142/s0217732319500962

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