THE INVESTIGATION OF A SET OF WEAKENED FIELD EQUATIONS FOR GENERAL RELATIVITY

摘要

General relativity is considered with an alternative set of field equations. These equations are weaker than the Einstein equations in the sense that spaces which are interpreted as the gravitational field in vacuo in the orthodox theory form only a sub-set of such spaces for these field equations. The discussion is confined to the case of the gravitational field in vacuo, hut in an appendix an introduction to the way in which matter is to he represented in the theory is given. Of particular interest are those spaces which are normally interpreted as giving a gravitational field in the presence of natter, but which here appear as the field in vacuo. General methods of constructing such spaces are given, and the metrics discussed on the assumption of particular symmetries. In addition, generalisations of such theorems as Birkhoff's, and that of Goldberg and Sachs are proved.nThe material forms part of a thesis submitted in 1962 for the Ph.D. degree of the University of London. This edited form has been prepared by C.W. Kilmister.