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.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.