A computer analysis of some of the Harrison metrics - Sadler, Christopher John (Rhodes University, Faculty of Science, Department of Mathematics, 1975)
In his paper B.K.Harrison concludes with the observation that his "solutions ... are presented as raw material for further research in General Relativity". In the same spirit, the present work started out as an attempt to process that raw material in a production-line powered by a computer. Harrison's solutions uould be fed in at one end, and the finished product, as yet undecided, would appear at the other. In the event, however, the project became more like an exercise in quality control, to continue the analogy. A search was made for algebraic criteria which would distinguish between those solutions which were acceptable for further analysis with particular regard to Gravitational radiation, and those which were not. Regrettably, no criteria could be found which characterised radiative solutions unequivocally, and, at the same time, lent themselves to a computer approach. The result is that the discussion of radiative solutions has had to be relegated to an appendix (Appendix 1), while the main body of the work is concerned with the determination of those quantities (the Newman-Penrose scalars) which would seem to be the foundation of any future computer-based analysis of gravitational radiation. Chapter 1 is an account of the underlying mathematical formulation, defining the terms, concepts and processes involved. In Chapter 2 the transformation of some of the ideas of Chapter 1 into computer software is presented. Chapter 3 is concerned with the specific metrics (the Harrison metrics) and the extent to which they have heen processed. The project has leaned heavily on papers by Harrison for the "raw material", by D' Inverno and Russell Clark, who pioneered the techniques and classified the Harrison metrics, and by Sachs for the treatment of gravitational radiation. However, the analysis of diagonal metrics, the special tetrad of Chapter 2 and the results in Appendix 2 are new.
Keywords: Computer science -- Mathematics; Software measurement