Viqar Husain

The Hamiltonian formulations of classical general relativity are used as the starting point for investigating specific questions associated with the quantization of gravity. (i) The ADM canonical formulation is used to study the effects of quantization on spacetime singularities present in the classical theory. In the context of a specific model, the Gowdy cosmology, the square of the curvature is computed as a quantum operator and its expectation values are calculated in quantum states of the model. It is found that there are no states for which the initial classical singularity present in the model ceases to exist. Thus, spacetime singularities appear to survive quantization. (ii) The same model and methods are used to investigate a conjecture due to Roger Penrose that associates gravitational entropy with the Weyl curvature. The expectation values of the square of the curvature operator are again calculated, this time in states corresponding to clumped and unclumped gravitons. It is found that the curvature can be used as a measure of the intrinsic entropy of the gravitational field. (iii) The recent canonical formulation of general relativity due to Ashtekar is used to carry out the Dirac quantization of the strong coupling limit of the theory. A complete set of commuting operators are found for this limit and these are used to construct explicitly a large set of quantum states that are annihilated by the constraints of the theory. It is shown that these states are also annihilated by the new form of the full Hamiltonian constraint. (iv) Finally, solutions to the Hamiltonian constraint that involve the holonomy of the Ashtekar connection, and are based on multiple loops that intersect at a point are described. This work is an extension of the work of Jacobson and Smolin who found solutions for one loop and two intersecting loops. It is shown that no solutions exist for three loops unless the tangent vectors to the loops at the intersection point are coplanar.