  We have shown recently that the gravity field phenomena can be described by a
traceless part of the wave-type field equation. This is an essentially
non-Einsteinian gravity model. It has an exact spherically-symmetric static
solution, that yields to the Yilmaz-Rosen metric. This metric is very close to
the Schwarzchild metric. The wave-type field equation can not be derived from a
suitable variational principle by free variations, as it was shown by Hehl and
his collaborates. In the present work we are seeking for another field equation
having the same exact spherically-symmetric static solution. The
differential-geometric structure on the manifold endowed with a smooth
orthonormal coframe field is described by the scalar objects of anholonomity
and its exterior derivative. We construct a list of the first and second order
SO(1,3)-covariants (one- and two-indexed quantities) and a quasi-linear field
equation with free parameters. We fix a part of the parameters by a condition
that the field equation is satisfied by a quasi-conformal coframe with a
harmonic conformal function. Thus we obtain a wide class of field equations
with a solution that yields the Majumdar-Papapetrou metric and, in
particularly, the Yilmaz-Rosen metric, that is viable in the framework of three
classical tests.
