eFTC-210301

Comparative Analysis and Complete Equivalence of Einstein and Yilmaz General Relativity
21 March 2021

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Abstract

In Einstein General Relativity, Newton's potential is solely identified in the context of weak gravitational fields. Here however, recalling strong support from accurate Doppler redshift measurements for the exponential multiplicative group property of the metric tensor, we analyze and compare both the Einstein and Yilmaz versions of General Relativity by making use of such an exponential metric parametrization with the Yilmaz tensor potentials as the physical degrees of freedom of the gravitational field for both theories. Through comparative analysis of the exterior and interior problems, it is shown that the Yilmaz version is completely equivalent to the Einstein version of General Relativity pending a re-definition (renormalization) of the matter energy-momentum tensor by including the effects of the gravitational energy-momentum tensor. To lowest order in Newton's constant, both theories are identical. In the Newtonian limit, the Yilmaz tensor potentials are mapped into Newton's potential and the Einstein gravitational energy-momentum pseudo-tensor is mapped into the Newtonian gravitational stress-energy tensor.

Copyright © 2021 Yvan Leblanc. All rights reserved

PACS: 4.60.+n, 11.17.+y, 97.60.Lf

Cite as: Leblanc, Y., "Comparative Analysis and Complete Equivalence of Einstein and Yilmaz General Relativity", manuscript no. eFTC-210301 (2021). http://www.efieldtheory.com/abs/?eFTC-210301; doi:10.13140/RG.2.2.11373.92640.