The method of recasting the Newman-Penrose formalism for the gravitational field equations into a Yang-Mills-type theory is reviewed. The free-field gravitational Lagrangian density structured along the lines of the free-field Yang-Mills Lagrangian density by Kibble is generalized to give the complete set of gravitational field equations one obtains in the Newman-Penrose formalism.

• Received 23 April 1971

DOI:https://doi.org/10.1103/PhysRevD.5.290