Table of contents

The work of Bowick and Rajeev (1987) and Pilch and Warner (1987) in constructing superstring vacuum bundles over Diff(S¹)/S¹ is generalised to Super-Diff(S¹)/S¹. The curvature of these bundles is shown to vanish in ten dimensions and, in the Ramond sector, not to depend on the 'sea level' of the ghosts.

An implementation of the time-dependent automorphism formalism for Bianchi cosmologies, in the computer algebra system SHEEP, is described. Its application to the particular case of Bianchi cosmologies admitting vacuum plane-wave solutions is given in relation to the equivalence problem. Using this approach, it is shown that the invariant characterisations of these metrics allow many properties of these spacetimes to be obtained in a straightforward manner. In particular, the invariant characterisations are used to determine the subclasses of spatially homogeneous vacuum plane-wave solutions which simultaneously admit distinct foliations with different Bianchi symmetries. The subclasses of the general vacuum plane-wave solution which admit a Bianchi group on a spacelike hypersurface are evaluated. These results are found to be expressible graphically, in the form of a phase plane which is physically interpretable as describing the amplitude and phase of polarisation of the plane wave. As a final application, it is shown that the Lifshitz-Khalatnikov Bianchi VI_h solution is the only vacuum plane-wave solution for which the gravitational wave is linearly polarised.

The construction of a configuration of scalar fields leading to an SU(8) charge obeying Gauss's law at infinity is investigated. It is shown that the infrared behaviour of the charge does not allow an asymptotically flat spacetime, a fact that seems applicable to any non-linear, non-compact sigma model.

Superstring theory entails a very close relationship between the linear connection of internal space and the gauge connection of the theory: the former is 'embedded' in the latter. The author interprets this to mean that the gauge bundle admits a sub-bundle which is isomorphic to the holonomy bundles of the linear connection. Thus it is important to have information on the holonomy group, not merely the holonomy algebra, which is controlled (via Iwamoto's theorem) by the Ricci form of a Kahler manifold. The author discusses Ricci-flat manifolds with holonomy group (Z_3m*SU(3))/Z₃ and explains the consequences for the grand unification sector of the theory.

Dirac quantisation of the G_N to infinity limit of general relativity is carried out. This is done in the framework of Ashtekar's new formulation of canonical gravity (1986). Using the new variables, a complete set of commuting operators are constructed for this limit. These operators are used to construct a large set of quantum states that are annihilated by the constraints (in this limit). It is shown that these states are also annihilated by the new form of the full Hamiltonian constraint.

Ashtekar's new Hamiltonian formulation of general relativity is derived starting from a complex covariant four-dimensional action principle. The action is a modification of the tetrad-Palatini action that results from splitting the connection into the self-dual and anti-self-dual pieces and keeping only the former.

Based on quantum electrodynamics in Robertson-Walker universes the author develops a general scheme for the calculation of the emission of a photon by an electron. Because Poincare invariance does not apply in a time-dependent gravitational field this decay is possible even as a first-order process which, indeed, is inseparably accompanied by the creation of electron-positron pairs and photons from vacuum. Therefore both processes are considered together in an 'added-up' probability. This is explicitly evaluated for a time-symmetrically expanding radiation-dominated Friedman universe.

The authors extend to dimensions greater than four, the canonical covariant formalism for the group manifold theories of supergravities, previously developed for gravity and simple supergravity in four dimensions. They give the d-dimensional properties for the form brackets and construct the Hamiltonian formalism for pure gravity in d dimensions and for d=5 supergravity. They also show that the formalism can be extended to supergravity theories constructed on free differential algebras.

The formalism of coset space dimensional reduction is extended to vielbein gauge fields, carrying both general coordinate and local Weyl transformations. Solutions of the CSDR constraints for BRST supersymmetry over a (D+2)-dimensional graded superspace (x^mu , theta , theta ) are superfields whose components are the usual vielbein, ghost and multiplier fields for general coordinate and Weyl invariance, plus an additional conventional scalar field. The Einstein action in D+2 dimensions reduces in D dimensions to that of a Dicke-Brans-Jordan model with a dimensionless coupling constant=1/2.

The author examines the most general theory describing a real scalar field coupled to Einstein gravity in four dimensions. The author shows that the stress tensor of the scalar field always has the structure of a fluid stress tensor. In the case that the scalar field is minimally coupled to gravity, this reduces to a perfect-fluid structure. In addition, the author obtains a generally non-trivial form of the Bianchi identities for this theory, investigates the kinematics of the scalar field and shows how to extend the analysis to include complex scalars and scalar multiplets. Finally, the author discusses the ground-state solutions of the theory, with special attention given to the case when the scalar field potential is polynomial in the fields. The author shows that the gravity-scalar coupling has interesting consequences for the spontaneous breakdown of gauge symmetries and for the observable value of the cosmological constant.

The authors consider the relation between a class of vacuum solutions in the Brans-Dicke theory of gravitation and perfect barotropic fluid Friedmann-Robertson-Walker cosmologies which can be related to five-dimensional vacuum solutions of Einstein's equations. They present a family of solitonic solutions of the Einstein equations obtained by the application of the inverse scattering technique in five dimensions followed by a subsequent Kaluza-Klein dimensional reduction procedure and a conformal rescaling. The effective energy-momentum tensor that appears is equivalent to that of the Brans-Dicke theory of gravitation. For large time values the metric approaches that of a flat FRW universe with a barotropic perfect fluid as material content. The solutions are a particular case of a family previously presented, together with a new renormalisation procedure for the inverse scattering technique.