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arXiv · 0801.2307

A modification of Einstein-Schrodinger theory that contains both general relativity and electrodynamics

J. A. Shifflett
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Abstract

We modify the Einstein-Schrodinger theory to include a cosmological constant $Λ_z$ which multiplies the symmetric metric, and we show how the theory can be easily coupled to additional fields. The cosmological constant $Λ_z$ is assumed to be nearly cancelled by Schrodinger's cosmological constant $Λ_b$ which multiplies the nonsymmetric fundamental tensor, such that the total $Λ=Λ_z+Λ_b$ matches measurement. The resulting theory becomes exactly Einstein-Maxwell theory in the limit as $|Λ_z|\to\infty$. For $|Λ_z|\sim 1/(Planck length)^2$ the field equations match the ordinary Einstein and Maxwell equations except for extra terms which are $<10^{-16}$ of the usual terms for worst-case field strengths and rates-of-change accessible to measurement. Additional fields can be included in the Lagrangian, and these fields may couple to the symmetric metric and the electromagnetic vector potential, just as in Einstein-Maxwell theory. The ordinary Lorentz force equation is obtained by taking the divergence of the Einstein equations when sources are included. The Einstein-Infeld-Hoffmann (EIH) equations of motion match the equations of motion for Einstein-Maxwell theory to Newtonian/Coulombian order, which proves the existence of a Lorentz force without requiring sources. This fixes a problem of the original Einstein-Schrodinger theory, which failed to predict a Lorentz force. An exact charged solution matches the Reissner-Nordstrom solution except for additional terms which are $\sim 10^{-66}$ of the usual terms for worst-case radii accessible to measurement. An exact electromagnetic plane-wave solution is identical to its counterpart in Einstein-Maxwell theory.

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J. A. Shifflett. 2008-02-08. A modification of Einstein-Schrodinger theory that contains both general relativity and electrodynamics. https://doi.org/10.1007/s10714-007-0572-6

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