A Class of Quasi-linear Equations in Coframe Gravity

Abstract

We have shown recently that the gravity fieldphenomena can be described by a traceless part of thewave-type field equation. This is an essentiallynon-Einsteinian gravity model. It has an exactsphericallysymmetric static solution, that yields to theYilmaz-Rosen metric. This metric is very close to theSchwarzchild metric. The wave-type field equation cannotbe derived from a suitable variational principle by free variations, as was shown by Hehl and hiscollaborators. In the present work we are looking foranother field equation having the same exactspherically-symmetric static solution. Thedifferential-geometric structure on the manifold endowed with a smoothorthonormal coframe field is described by the scalarobjects of anholonomity and its exterior derivative. Weconstruct a list of the first and second order SO(1,3)-covariants (one- and two-indexedquantities) and a quasi-linear field equation with freeparameters. We fix a part of the parameters by acondition that the field equation is satisfied by aquasi-conformal coframe with a harmonic conformal function .Thus we obtain a wide class of field equations with asolution that yields the Majumdar-P apapetrou metricand, in particular, the Yilmaz-Rosen metric, that is viable in the framework of three classicaltests.