A spin coefficient approach to vacuum quadratic Poincaré gauge field theory
The field equations of the vacuum Quadratic Poincare Gauge Field Theory are expressed in the spin coefficient formalism of Newman and Penrose. These equations are differential identities involving the curvature and torsion, and in this NewmanPenrose type approach must be combined with the generalized Newman-Penrose identities given in chapter 4. The use of this Newman-Penrose type formalism is demonstrated in the derivation of several new classes of exact solutions which would have been impossible to obtain by the various methods being used at this moment in time. This therefore demonstrates the power of the spin coefficient formalism developed in chapter 6. A brief look at SO(3) symmetric space-times, in the context of the vacuum Quadratic Poincare Gauge Field Theory, is taken in chapter 11. As a final consideration, a deeper look at the vacuum Quadratic Poincare Gauge Field Theory itself is taken, in order to see whether or not it is a reasonable Theory of Gravitation.