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Abstract: In the purely affine formulation of gravity, the gravitational field isrepresented by the symmetric part of the Ricci tensor of the affine connection.The classical electromagnetic field can be represented in this formulation bythe second Ricci tensor of the connection. Such a construction is dynamicallyequivalent to the sourceless Einstein-Maxwell equations. We generalize thisconstruction to the case with sources, represented by the derivative of theaffine Lagrangian density with respect to the connection. We show that theMaxwell equations with sources emerge for the simplest affine Lagrangian formatter, while the Einstein and Lorentz equations arise if mass haselectromagnetic origin. We also show that the Maxwell equations replace theunphysical constraint imposed by the projective invariance of purely affineLagrangians that depend explicitly on the connection.



Author: Nikodem J. Poplawski

Source: https://arxiv.org/







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