General Relativity and Gravitation

, Volume 40, Issue 8, pp 1745–1769

A modification of Einstein–Schrödinger theory that contains both general relativity and electrodynamics

Research Article


We modify the Einstein–Schrödinger theory to include a cosmological constant Λz which multiplies the symmetric metric, and we show how the theory can be easily coupled to additional fields. The cosmological constant Λz is assumed to be nearly cancelled by Schrödinger’s cosmological constant Λb which multiplies the nonsymmetric fundamental tensor, such that the total ΛΛzΛb matches measurement. The resulting theory becomes exactly Einstein–Maxwell theory in the limit as |Λz| → ∞. For |Λz| ~ 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–Schrödinger theory, which failed to predict a Lorentz force. An exact charged solution matches the Reissner–Nordström solution except for additional terms which are ~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.


Einstein–Schrodinger theory Einstein–Straus theory Cosmological constant 


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Copyright information

© Springer Science+Business Media, LLC 2007

Authors and Affiliations

  1. 1.Department of PhysicsWashington UniversitySt LouisUSA

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