ISSN:
1089-7658
Source:
AIP Digital Archive
Topics:
Mathematics
,
Physics
Notes:
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 and quadratic in the first order derivatives of the coframe, both with coefficients that depend on the coframe variables. The article 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 three classical tests) indistinguishable from Einstein field equations. This family also includes, of course, Einstein equations. Moreover, it is shown, explicitly, how to exhibit it. The basic tool employed in the article 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. © 2000 American Institute of Physics.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1063/1.1287434
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