On a class of invariant coframe operators with application to gravity

Abstract

Let a differential 4D-manifold with a smooth coframe field be given. Consider the operators on it that are linear in the second order derivatives or quadratic in the first order derivatives of the coframe, both with coefficients that depend on the coframe variables. The paper exhibits the class of operators that are invariant under a general change of coordinates, and, also, invariant under the global SO(1,3)-transformation of the coframe. A general class of field equations is constructed. We display two subclasses in it. The subclass of field equations that are derivable from action principles by free variations and the subclass of field equations for which spherical-symmetric solutions, Minkowskian at infinity exist. Then, for the spherical-symmetric solutions, the resulting metric is computed. Invoking the Geodesic Postulate, we find all the equations that are experimentally (by the 3 classical tests) indistinguishable from Einstein field equations. This family includes, of course, also Einstein equations. Moreover, it is shown, explicitly, how to exhibit it. The basic tool employed in the paper is an invariant formulation reminiscent of Cartan's structural equations. The article sheds light on the possibilities and limitations of the coframe gravity. It may also serve as a general procedure to derive covariant field equations.

References in corpus (7)

• Symmetric teleparallel general relativity
• General relativity on a null surface: Hamiltonian formulation in the teleparallel geometry
• The quadratic spinor Lagrangian is equivalent to the teleparallel theory
• A small guide to variations in teleparallel gauge theories of gravity and the Kaniel-Itin model
• Sparling two-forms, the conformal factor and the gravitational energy density of the teleparallel equivalent of general relativity
• Gravity on a parallelizable manifold. Exact solutions
• A class of quasi-linear equations in coframe gravity

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• Conserved currents for general teleparallel models
• Maxwell-type behaviour from a geometrical structure
• An assessment of Evans' unified field theory I
• An assessment of Evans' unified field theory II