A class of quasi-linear equations in coframe gravity

TL;DR

This paper introduces a new class of quasi-linear field equations in coframe gravity that admit solutions close to classical metrics like Schwarzschild and Yilmaz-Rosen, expanding the theoretical framework beyond Einstein's gravity.

Contribution

It constructs a family of quasi-linear field equations in coframe gravity with specific solutions matching known metrics, without deriving from a variational principle.

Findings

The equations admit the Yilmaz-Rosen and Majumdar-Papapetrou metrics.

The proposed models are consistent with the three classical tests of gravity.

A wide class of solutions is obtained by fixing parameters based on geometric conditions.

Abstract

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.