Foundations of Physics Letters

, Volume 16, Issue 4, pp 369–377 | Cite as

A Generally Covariant Field Equation for Gravitation and Electromagnetism

  • Myron W. Evans


A generally covariant field equation is developed for gravitation and electromagnetism by considering the metric vector qμ in curvilinear, non-Euclidean spacetime. The field equation is
$$R^\mu - {\text{ }}\frac{1}{2}Rq^\mu = kT^\mu ,$$
, where Tμ is the canonical energy-momentum four-vector, k the Einstein constant, Rμ the curvature four-vector, 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 qμ. Generally covariant electromagnetism is described by multiplying the foregoing on both sides by the wedge qν. Therefore, gravitation is described by symmetric metricqμqν and electromagnetism by the anti-symmetric defined by the wedge product qμqν.
generally covariant field equation for gravitation and electromagnetism O(3) electrodynamics B(3) field 


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  1. 1.
    E. G. Milewski, The Vector Analysis Problem Solver (Research and Education Association, New York, 1987).Google Scholar
  2. 2.
    A. Einstein, The Meaning of Relativity (Princeton University Press, 5th edn. 1955).Google Scholar
  3. 3.
    M. W. Evans, J.-P. Vigier, et al., The Enigmatic Photon (Kluwer Academic, Dordrecht, 1994 to 2002, hardback and paperback), Vols. 1–5.CrossRefGoogle Scholar
  4. 4.
    M. W. Evans and L. B. Crowell, Classical and Quantum Electrodynamics and the B (3) Field (World Scientific, Singapore, 2001).MATHGoogle Scholar
  5. 5.
    M. W. Evans and A. A. Hasanein, The Photomagneton in Quantum Field Theory (World Scientific, Singapore, 1994).Google Scholar
  6. 6.
    M. W. Evans and S. Kielich, eds., Modern Non-Linear Optics, in I. Prigogine and S. A. Rice, series eds., Advances in Chemical Physics (Wiley Inter-Science, New York, 1995 to 1997, hardback and paperback), Vol. 85, 1st edn.Google Scholar
  7. 7.
    M. W. Evans, ed., 2nd edn. of S. A. Rice, series eds., Advances in Chemical Physics Ref. 6, Vol. 119 (Wiley Inter-Science, 2001).Google Scholar
  8. 8.
    L. H. Ryder, Quantum Field Theory, 2nd edn. (Cambridge University Press, 1987 and 1996).Google Scholar
  9. 9.
    M. Sachs in S. A. Rice, series eds., Advances in Chemical Physics (Wiley Inter-Science, 2001) Ref. 7, Vol. 119(1), and references therein.Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Myron W. Evans
    • 1
  1. 1.Institute for Advanced StudyAlpha FoundationHungary

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