Relativistic cosmology and some related problems in general relativity theory

Abstract

The main part of this thesis (Chapters A, B, C, D) deals with the cosmological problem and the use of quadruplet vector-fields in describing the continuous creation of matter postulated in recent cosmological investigations. Chapter E includes a discussion of previous attempts to generalize the relativistic theory of gravitation, and a further application of quadruplet vector-fields in formulating a 'unified' field-theory. For this reason, it has been added to the previous chapters to constitute Part I of the thesis, Part II includes two other special problems in general relativity theory: the "clock paradox" and the gravitational rod-shift. Most of the original work presented in this thesis is contained in chapters D, E of Part I and in the two chapters A, B of Part II, The work in the earlier chapters, especially that in chapter B of Part I (which is wholly devoted to the geometrical study of quadruplet vector-fields), necessitates the summarizing of earlier work onthe subject. During this summarizing, some earlier work has been developed, especially in sections 10 and 11 dealing with the derivation of second order tensors for quadruplet-fields; some results have been reproduced by using different methods and sometimes under less restrictive conditions in particular the derivation of the Robertson metric' given in section 16; other results are readjusted in view of later work in particular the conditions of the equivalence of two quadruplets given in section 8 and the fundamental equations of an 'automorphism' and those of a group of motions in a 'quadruplet-space' given in section 14. Some new results have also been obtained through this work, in particular the set of 'hermitian' and 'anti-hermitian' tensors given in section 12 and the conditions for the quadruplet-vectors to form a group of motions given in section 14. When indebted to other writers, such indebtedness is fully indicated, both in the text of the thesis and in the list of references given at the end of each chapter. The main substance of the "clock paradox" problem (Chapter A of Part II) has been accepted for publication in the Proceedings of the Cambridge Philosophical Society, Another paper on the applications of quadruplet vector-fields in relativity theory is being prepared in collaboration with Professor W.H. McCrea. The candidate also hopes to use some other parts of the present thesis, especially those dealing with the derivation of the various tensors for the quadruplet-space, the groups of motions in this space, and the calculation of the gravitational red-shift in general, as bases for other papers.