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Abstract: In this paper we present a theory of the gravitational field where this fielda kind of square root of g is represented by a 1,1-extensor field hdescribing a plastic distortion of the Lorentz vacuum a real substance thatlives in a Minkowski spacetime due to the presence of matter. The field hdistorts the Minkowski metric extensor in an appropriate way see belowgenerating what may be interpreted as an effective Lorentzian metric extensor gand also it permits the introduction of different kinds of parallelism rules onthe world manifold, which may be interpreted as distortions of the parallelismstructure of Minkowski spacetime and which may have non null curvature and-ortorsion and-or nonmetricity tensors. We thus have different possible effectivegeometries which may be associated to the gravitational field and thus itsdescription by a Lorentzian geometry is only a possibility, not an impositionfrom Nature. Moreover, we developed with enough details the theory of multiformfunctions and multiform functionals that permitted us to successfully write aLagrangian for h and to obtain its equations of motion, that results equivalentto Einstein field equations of General Relativity for all those solutionswhere the manifold M is diffeomorphic to R^4. However, in our theory,differently from the case of General Relativity, trustful energy-momentum andangular momentum conservation laws exist. We express also the results of ourtheory in terms of the gravitational potential 1-form fields living inMinkowski spacetime in order to have results which may be easily expressedwith the theory of differential forms. The Hamiltonian formalism for our theoryformulated in terms of the potentials is also discussed. The paper containsalso several important Appendices that complete the material in the main text.

Autor: Virginia V. Fernandez, Waldyr A. Rodrigues Jr


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