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Einstein General Relativity In Bi-metric Spacetime Contains Exponential Metrics Which Dynamically Preserve Bi-metric "Light Cone Causality"

Darryl J. Leiter·Stanley L. Robertson
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Abstract

It is well known that Einstein General Relativity can be expressed covariantly in bi-metric spacetime, without the uncertainties which arise from the effects of gravitational energy-momentum pseudo-tensors. However the effect that the Strong Principle of Equivalence (SPOE) has on the curved and flat bi-metric spacetime tetrad structure has not been fully explored. In the context of bi-metric General Relativity the (SPOE) requires that: a) in the absence of gravitation due to spacetime curvature a Global Inertial Cartesian Minkowski (GICM) spacetime frame exists in which Special Relativity is valid and, b) in the presence of gravitation due to spacetime curvature a bi-metric Local Free Fall frame (LFF) must always exist. These two conditions required by the (SPOE) are then shown to imply that a symmetric gravitational potential tensor must exist in the bi-metric spacetime which is connected exponentially to the tetrad inner product between the curved symmetric tetrads and the flat background symmetric tetrads. It is then shown that this (SPOE) generated gravitational potential tensor has the property of exponentially connecting the curved metric tensor with the flat background metric tensor in a manner which allows the condition of "Light Cone Causality" (LCC) to be dynamically satisfied in the bi-metric spacetime. Substitution of this (LCC) conserving exponential metric into the bi-metric Einstein field equations, subject to an appropriate choice of tensor gauge conditions, yields an equivalent set of (LCC) conserving bi-metric Einstein field equations for the gravitational potential tensor, the full implications of which will be explored in future papers.

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BibTeXRIS

Darryl J. Leiter, Stanley L. Robertson. 2003-07-16. Einstein General Relativity In Bi-metric Spacetime Contains Exponential Metrics Which Dynamically Preserve Bi-metric "Light Cone Causality". https://arxiv.org/abs/gr-qc/0101025

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