A Generally Covariant Field Equation for Gravitation and Electromagnetism
 Myron W. Evans
 … show all 1 hide
Rent the article at a discount
Rent now* Final gross prices may vary according to local VAT.
Get AccessAbstract
A generally covariant field equation is developed for gravitation and electromagnetism by considering the metric vector q ^{μ} in curvilinear, nonEuclidean spacetime. The field equation is $$R^\mu  {\text{ }}\frac{1}{2}Rq^\mu = kT^\mu ,$$ , where T ^{μ} is the canonical energymomentum fourvector, k the Einstein constant, R ^{μ} the curvature fourvector, and R the Riemann scalar curvature. It is shown that this equation can be written as $$T^\mu = \alpha q^\mu ,$$ where α is a coefficient defined in terms of R, k, and the scale factors of the curvilinear coordinate system. Gravitation is described through the Einstein field equation, which is recovered by multiplying both sides by q ^{μ}. Generally covariant electromagnetism is described by multiplying the foregoing on both sides by the wedge q ^{ν}. Therefore, gravitation is described by symmetric metricq ^{μ} q ^{ν} and electromagnetism by the antisymmetric defined by the wedge product q ^{μ} q ^{ν}.
 E. G. Milewski, The Vector Analysis Problem Solver (Research and Education Association, New York, 1987).
 A. Einstein, The Meaning of Relativity (Princeton University Press, 5th edn. 1955).
 M. W. Evans, J.P. Vigier, et al., The Enigmatic Photon (Kluwer Academic, Dordrecht, 1994 to 2002, hardback and paperback), Vols. 1–5.
 M. W. Evans and L. B. Crowell, Classical and Quantum Electrodynamics and the B ^{(3)} Field (World Scientific, Singapore, 2001).
 M. W. Evans and A. A. Hasanein, The Photomagneton in Quantum Field Theory (World Scientific, Singapore, 1994).
 M. W. Evans and S. Kielich, eds., Modern NonLinear Optics, in I. Prigogine and S. A. Rice, series eds., Advances in Chemical Physics (Wiley InterScience, New York, 1995 to 1997, hardback and paperback), Vol. 85, 1st edn.
 M. W. Evans, ed., 2nd edn. of S. A. Rice, series eds., Advances in Chemical Physics Ref. 6, Vol. 119 (Wiley InterScience, 2001).
 L. H. Ryder, Quantum Field Theory, 2nd edn. (Cambridge University Press, 1987 and 1996).
 M. Sachs in S. A. Rice, series eds., Advances in Chemical Physics (Wiley InterScience, 2001) Ref. 7, Vol. 119(1), and references therein.
 Title
 A Generally Covariant Field Equation for Gravitation and Electromagnetism
 Journal

Foundations of Physics Letters
Volume 16, Issue 4 , pp 369377
 Cover Date
 20030801
 DOI
 10.1023/A:1025365826316
 Print ISSN
 08949875
 Online ISSN
 15729524
 Publisher
 Kluwer Academic PublishersPlenum Publishers
 Additional Links
 Topics
 Keywords

 generally covariant field equation for gravitation and electromagnetism
 O(3) electrodynamics B (3) field
 Authors

 Myron W. Evans ^{(1)}
 Author Affiliations

 1. Institute for Advanced Study, Alpha Foundation, Hungary