eFTC-230201

Einstein Real Gravity Beyond The Newton Gauge
12 February 2023

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Abstract

We derive the gravitational field equations in orthogonal curvilinear coordinates for a time-dependent isotropic metric and a slow moving fluid matter source in Einstein Real Gravity (RG) beyond the Newton gauge. When using a Yilmaz-like exponential parametrization for the metric tensor, the Newton potential is no longer solely given by the 00-component of the tensor potentials as it is shifted in components space, thus compelling us to re-define the parametrization in such a way as to lock the Newton potential on the 00-component. Making use of the new parametrization, we re-derive the gravitational field equations, the Freud-Euler equation for the fluid source as well as the modified Tolman-Oppenheimer-Volkoff hydrostatic formula for star equilibrium. We also check the algebraic equivalence of the Real Gravity and traditional curvature formulations for the case of an isotropic spherically symmetric metric. Although algebraically equivalent, their physics is not since the gravitational field is described by the tensor potentials in Einstein Real Gravity instead of the metric tensor. For weak fields, they are indistinguishable but at strong fields, they are very different as no black holes exist in Einstein Real Gravity.

Copyright © 2023 Yvan Leblanc. All rights reserved

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

Cite as: Leblanc, Y., "Einstein Real Gravity Beyond The Newton Gauge", Report no. eFTC-230201 (2023). http://www.efieldtheory.com/abs/?eFTC-230201; doi:10.13140/RG.2.2.35792.38405.