Note onSL(2, C)gauge theory of gravitation

A previous paper suggested a Lagrangian density to the $\mathrm{SL}(2, C)$ gauge theory of general relativity that leads to the Bianchi equations of the Newman-Penrose equations. In this paper we propose a new Lagrangian density that also leads to the Bianchi equations, but with matter already substituted for nine of the ten components of the Ricci tensor, thus incorporating nine out of the ten Einstein conditions.