General Relativity and Gravitation

, Volume 14, Issue 4, pp 309–330 | Cite as

The generalized Einstein-Maxwell theory of gravitation

  • V. N. Ponomariov
  • Ju. Obuchov
Research Articles

Abstract

A new Lagrangian theory of gravitation in which the metric and the arbitrary affine connection are regarded as independent field variables has been considered. Making use of the pure geometrical objects only from the variational principle the empty field equations are derived. It is shown that the metric obeys the ordinary Einstein equations of general relativity. However, the covariant derivative of the metric tensor does not vanish, so that the vector's length is generally nonintegrable under the parallel displacement. The torsion trace vector turns out to be the natural dynamical variable, satisfying the Maxwell-like equations with tensor of homothetic curvature as the Maxwell tensor. The equations of motion are explored; they are shown to be identical to the motion of electric charge under the Lorentz force. The conservation laws are discussed.

Keywords

Variational Principle Covariant Derivative Einstein Equation Lorentz Force Dynamical Variable 

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Copyright information

© Plenum Publishing Corporation 1982

Authors and Affiliations

  • V. N. Ponomariov
    • 1
  • Ju. Obuchov
    • 1
  1. 1.Department of Theoretical PhysicsMGU Moscow State UniversityMoscowUSSR

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