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One of Julian Barbour’s main aims is to solve the problem of time that appears in quantum geometrodynamics (QG). QG involves the application of canonical quantization procedure to the Hamiltonian formulation of General Relativity. The problem of time arises because the quantization of the Hamiltonian constraint results in an equation that has no explicit time parameter. Thus, it appears that the resulting equation, as apparently timeless, cannot describe evolution of quantum states. Barbour attempts to resolve the problem by allegedly eliminating time from his interpretation of QG. In order to evaluate the efficacy of his solution, it is necessary to ascertain in what sense time has been eliminated from his theory. I proceed to do so by developing a form of conceptual analysis that is applicable to the concept of time in physical theories and applying this analysis to Barbour’s account.

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This thesis contains two main areas of research in General Relativity Theory. These are the study of the sectional curvature function in general relativity and the study of symmetries. The sectional curvature function is a real-valued map defined on the set of all non-null 2-spaces at a certain point in the space-time. several results relating to the sectional curvature function will be given. The bivector curvature function will then be defined as the extension of the sectional curvature function to the set of all "non-null" bivectors at a point in the space-time. Two important results relating to this function will be proved. Symmetries in general relativity have been widely researched. In this thesis, three results on symmetries will be proved. Firstly, it will be shown that there exists a space-time admitting a finite-dimensional curvature collineation algebra not equal to the affine algebra. Then a result on the conformal algebra in a 2-dimensional manifold will be given. Lastly, a proof will be given on the dimension of the sectional curvature preserving algebra.

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The general theory of relativity is used to investigate the properties and behaviour of spherically symmetrical masses of perfect fluid. The stability of equilibrium models against adiabatic radial perturbations is investigated, and a new derivation is given of Chandrasekhar's well-known equation for the normal modes of oscillation. The behaviour near the centre of various parameters suggests a simple formula for the frequencies of these normal modes. The study of spherically symmetrical bodies in radial motion under adiabatic conditions is greatly simplified if we assume that a certain mathematical condition is satisfied, the physical consequences of which are found to be not unduly restrictive. In particular, this condition is satisfied if the density is uniform through-. out the body at each instant, and a differential equation can then be derived for the radius in terms of the mass and the (arbitrary) equation of state of the material at the centre. It follows that, if the body contracts to a radius less than 9GM/4C2 it must eventually collapse to a point singularity if infinite density. This conclusion is also shown to be valid for any body that shrinks to a radius less than 2GM/C2, whatever the equation of state. Non-adiabatic radial motions are studied with the help of a particular analytical solution, the physical significance of which is discussed. It is shown that, once the radius has shrunk to less than 2GM/C2 collapse cannot be avoided even by the complete conversion of matter into radiation. It is also found that, if the motion is quasi-static, certain bodies will settle into a stable state of expansion, while in others an instability could develop, and result in rapid expansion. Finally, it is shown that if the radial motion remains sufficiently slow, collapse can always be avoided, provided that the system radiates energy sufficiently rapidly.