City Research Online

Abstract

Theoretical objections to the concept of a spacetime singularity and the scanty, and sometimes controversial, nature of the available experimental data concerning the existence of black holes, has heightened interest in the search for viable, non-singular alternatives to Einstein's theory of gravitation. One way of developing such alternatives is to perturb or deform the solution spacetimes of the Einstein model in such a manner that essential singularities are either eliminated or avoided, but useful features, such as the weak-field predictions, are retained. The aim of the present work is to study the feasibility of such a programme, and to analyse and classify some of the possible perturbations.

Our approach to the problem is novel for this field of work, the objective being to associate dynamical systems with the flows of the geodesic equations. Since dynamical systems are defined: for all values of the flow parameter, the proper-time in our case, the resulting geodesic flows will be complete. This means that any singularities on the original manifolds will either be changed into regular or critical points, or isolated by critical sets in which case they are effectively disconnected from the spacetimes of all observers.

The thesis commences with a general introduction in which we discuss the pros and cons of the singularity argument and motivate our approach. In chapter 2 we review the Einstein model, paying particular attention to the definitions and proofs of the singularity theorems, while chapter 3 is devoted to a presentation of those aspects of dynamical systems theory which are needed for our purposes. However, since the latter is not a subject which is
usually associated with conventional gravitation theory, we have attempted to make this presentation more or less self-contained.

The next three chapters contain our new results. Thus, in chapter 4 we 'translate' the singularity theorems into the language of dynamical systems theory and examine their possible breakdown, Then, in chapters 5 and 6, we construct and analyse several amended versions of Newtonian and Schwarzschild gravitation respectively; the Newtonian amendments being necessary to preserve the use of the Newtonian limit as a boundary condition. Finally, in chapter 7, we discuss the physical interpretation of our results and assess the viability of the method used.

Publication Type:	Thesis (Doctoral)
Subjects:	Q Science Q Science > QA Mathematics Q Science > QB Astronomy Q Science > QC Physics
Departments:	School of Science & Technology > Department of Mathematics School of Science & Technology > School of Science & Technology Doctoral Theses Doctoral Theses

Export

Downloads