Problems in relativistic cosmology

Abstract

This thesis is concerned with the study of two inter-related topics: the existence and propertiesof horizons, boundaries and barriers in cosmological models and the information that an observer in a certain model may, in principle, gain about his universe. Accordingly, it deals first with concepts of uncertainty and indeterminacy in cosmology (Chapter I).In Chapter II, sections (i), (ii), (iii), (vi) and (vii) introduce and summarise earlier work on the subject of event and particle horizons in homogeneous and isotropic world-models; the remainder of the chapter discusses certain features and develops various problems which arise from this, during the course of which is introduced the new notion of the degenerate (invariant) horizon. Chapter III is concerned with the "Milne-type" boundary and discusses the boundary of distance by parallax. It is shown that the boundary in Milne's model is a degenerate particle horizon.The behaviour of observables in the neighbourhood of an event horizon or a particle horizon is examined for five expanding model universes of the Robertson-Walker type, and for their duals, obtained by time-reversal; the results are demonstrated diagram-matically (Chapter IV). This examination paves the way for, and finds application in, Chapter V which investigates information theory in cosmological models and studies in particular the rate of flow, and hence the rate of loss, of information in the models considered; the influence of the existence or otherwise of horizons is explicitly demonstrated. The two remaining chapters (VI, VII) investigate the nature of the singularity at r = 2m in the Schwarzschild space-time, in the Finkelstein spacetime obtained by transformation from Schwarzschild's metric, and also in the space-time obtained by time-reversal of the Finkelstein metric. By studying the amount of information which an observer in the region r>2m may in principle receive from r< 2m from light signals or probes, it is shown (Chapter VI) that the surface r = 2m in the Schwarzschild space-time is a barrier which is a degenerate event horizon for such an observer. Chapter VI concludes by considering Darwin's work on the manifestation of the singularity in the presence of a neighbouring star and of a star-field background.In Chapter VII, it is shown that the barrier at r = 2m in the Finkelstein space-time is not a degenerate event horizon for the observer in r>2m, but that, in contrast, it is a degenerate event horizon in the time-reversed case. This topic is completed by an investigation of the transformations concerned to discover to what extent they are valid and to demonstrate how this difference arises.