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

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

2008-01-15

arxiv.org/abs/0801.2307v2

Gen.Rel.Grav.40:1745-1769,2008

Astronomy and Astrophysics

Astrophysics

General Relativity and Quantum Cosmology

fixed 2 references, accepted by "General Relativity and Gravitation"

Scientific paper

10.1007/s10714-007-0572-6

We modify the Einstein-Schrodinger theory to include a cosmological constant $\Lambda_z$ which multiplies the symmetric metric, and we show how the theory can be easily coupled to additional fields. The cosmological constant $\Lambda_z$ is assumed to be nearly cancelled by Schrodinger's cosmological constant $\Lambda_b$ which multiplies the nonsymmetric fundamental tensor, such that the total $\Lambda=\Lambda_z+\Lambda_b$ matches measurement. The resulting theory becomes exactly Einstein-Maxwell theory in the limit as $|\Lambda_z|\to\infty$. For $|\Lambda_z|\sim 1/(Planck length)^2$ 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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