Metric-Torsional Conformal Gravity

TL;DR

This paper develops a new metric-torsional conformal curvature in geometric backgrounds with torsion, providing a conformally invariant curvature that includes both metric and torsional degrees of freedom, along with consistent field equations.

Contribution

It introduces the first combined metric-torsional conformal curvature and derives a consistent set of field equations for this new geometric structure.

Findings

Constructed a metric-torsional conformal curvature tensor.

Derived the most general action and field equations.

Verified conservation laws and trace conditions.

Abstract

When in general geometric backgrounds the metric is accompanied by torsion, the metric conformal properties should correspondingly be followed by analogous torsional conformal properties; however a combined metric torsional conformal structure has never been found which provides a curvature that is both containing metric-torsional degree of freedom and conformally invariant: in this paper we construct such a metric-torsional conformal curvature. We proceed by building the most general action, then deriving the most general system of field equations; we check their consistency by showing that both conservation laws and trace condition are verified. Final considerations and comments are outlined.