Does the coframe geometry can serve as a unification scheme?

TL;DR

This paper explores the coframe geometry as a potential unification scheme for gravity and electromagnetism, showing that under certain conditions, the coframe field exhibits Maxwell-like behavior alongside gravity.

Contribution

It constructs a general family of connections in coframe geometry and demonstrates that Maxwell equations emerge as invariance conditions, linking electromagnetism to gravity within this framework.

Findings

Coframe connections include Levi-Civita and Weitzenböck as special cases.

Maxwell equations are necessary and sufficient for invariance of the coframe action.

Coframe field exhibits Maxwell-type behavior in viable models.

Abstract

The coframe field model is known as a viable model for gravity. The principle problem is an interpretation of six additionaldegrees of freedom. We construct a general family of connections which includes the connections of Levi-Civita and Weitzenb\"{o}ck as the limiting cases. We show that for a special choice of parameters, a subfamily of connections is invariant when the infinitesimal field of transformations (antisymmetric tensor) satisfies the pair of vacuum Maxwell equations -- one for torsion and one for non-metricity. Moreover, the vacuum Maxwell equations turn to be the necessary and sufficient conditions for invariance of the viable coframe action (alternative to GR). Consequently, for the viable models, the coframe field is proved to have the Maxwell-type behavior in addition to the known gravity sector.