Dolan, Patrick (1964)
Problems in relativistic and steady-state cosmology.
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This thesis consists of four chapters. Chapter I. The conceptual problems that arise from the use of the calculus of variations in Riemannian spaces are stated and solved, with topological significance indicated. A derivation of the identities satisfied by every scalar field is given in detail and the similarity of this to certain results of C.Lanczos is shown. Worked examples are given. Chapter II. The derivation of the matter tensor for an ideal fluid from a variational integral and its physical interpretation are given. This puts earlier work of G. Marx on a fairly rigorous basis. A literature survey is included. Chapter III. The relativistic model of the steady state theory of cosmology of W. H. McCrea is derived and discussed in the light of critical work by W. B. Bonnor and P. Roman. The notions of indeterminate fluid velocity vector fields and of more than one gravitational mass density are considered at great length here. Chapter IV.An axiomatic formulation of the electrical universe of R. A. Lyttleton and H. Bondi is given. It is shown that the cosmology is the same as that of Chapter III with the electromagnetic interpretation of the matter's motion not strictly necessary. A newtonian universe based on a universal excess of positive charge is discussed in an appendix. This chapter is the work of both Professor W. H. McCrea, F.R.S., and myself.
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Institution: University of London, Royal Holloway College (United Kingdom).