Table of contents

The authors present a general solution of the equations of motion for a classical relativistic string in Minkowski space. For an 'open' string the solution is determined by a single real null curve which satisfies a quasiperiodicity condition. A formula is deduced which generates all such curves in terms of freely specifiable functions. For a 'closed' string two such curves are required. Their theory establishes a rigorous basis for the numerical investigation of 'cosmic strings', and also forms a starting point for a constraint-free Lorentz covariant analysis of the quantum relativistic theory.

The generalised Kerr-Schild transformation on a vacuum background is used to generate exact solutions of Einstein-Maxwell field equations. Two families of algebraically general solutions are obtained. For generic values of a certain parameter a, they consist of the homogeneous non-static metrics given by Datta (1965). For a=1+or-2, there are solutions with only two commuting spacelike Killing vectors.

Using the positive-mass theorem the author shows the uniqueness of a static stellar model, provided the equation of state is such that d rho /dp is small in some sense and provided there exists a spherically symmetric stellar model with the same equation of state and surface potential.

This paper investigates the possibility of eliminating the supertranslation gauge freedom at scri by the introduction of a unique set of sections, which may be understood as giving a centre of mass system of reference. The construction depends on the properties of the physical system at the fixed retarded time defined by these sections.

A comprehensive approach to the problem of constructing a consistent classical field theory of interacting higher-spin gauge fields is presented. BRST techniques are used similar to those used in covariant string field theory. A part of the cubic vertex is derived and shown to reproduce the cubic Yang-Mills interaction. Further progress is halted by a lack of an effective way to calculate the full vertex. There are indications that the theory, as presented, might only be consistent in four spacetime dimensions.

The thermodynamics and cosmology of torus-compactified heterotic strings are studied. The authors emphasise qualitatively new effects due to compactification. New topologically stable states appear which correspond to strings winding around the non-simply-connected compact manifold. Under reasonable assumptions they avoid the blowing up of the compactification scale when the universe becomes matter dominated. For a higher-dimensional point field theory with a scale-invariant ground state this blowing up would be unavoidable.

The authors obtain the radial decoupled equation for the electromagnetic perturbations of the NUT-de Sitter spacetime. They then reduce the radial equation to a one-dimensional wave equation with real short-range potential and show that the superradiance phenomenon occurs.

Barrow and Sonoda (1986) have investigated the stability, at large time, of certain Bianchi universes. Their method involves studying a set of first-order differential equations which governs the evolution of the three principal expansion rates, and the conservation equations. This set of equations is not in general equivalent to Einstein's equations; in some cases it may be a subset, or an asymptotic approximation. The results given by Barrow and Sonoda refer to the stability of exact solutions of the Einstein equations with respect to perturbations which are governed by this set of first-order equations, rather than by Einstein's equations. The authors show that the results obtained in this way do not reliably determine whether a spacetime is stable to perturbations which evolve according to the full and exact Einstein equations.

In the framework of the Einstein-Cartan theory (ECT) with a Dirac field as source, the authors find an exact cylindrically symmetric solution, where the Dirac field has to fulfil certain algebraic constraints. Moreover, turning to the Poincare gauge theory (PGT), with a Lagrangian which is at most quadratic in torsion and curvature, they find a related exact solution. The tetrad and the spinor fields are the same as in the Einstein-Cartan case and the torsion is also proportional to the spin current.

The equation of deviation is derived for a conformally invariant theory of gravitation and electromagnetism in which scale is generated by a topological constraint. Compared with its counterpart in the Einstein-Maxwell theory, the equation contains some extra terms proportional to the electromagnetic potential indicating the existence of linear and non-linear Bohm-Aharonov effects. These are present also in the related theories of Weyl and Dirac. From the same equation one can derive an expression for the quantisation of geometry which further illustrates the topological mechanism for the genesis of scale. As a by-product, the magnitudes of some Einstein-Maxwell corrections in Weber-type experiments are estimated.

Formulae for calculating the radial and the axial Newtonian gravitational forces of a finite cylinder are given. Some applications of these formulae in physics and geophysics are shown.

The effect of spontaneous symmetry breaking by gravitational field is investigated in the case of open homogeneous isotropic models within the framework of the Poincare gauge theory of gravity. It is shown that this procedure permits the construction of cosmological models that are regular in the metric and the torsion.

A metric-affine geometrical structure is used to formulate a generalised theory of gravity, in which the motion of a test particle is characterised by a finite proper acceleration in the local tangent space. According to the local equivalence, valid for quantum systems, between acceleration and temperature, the theory is thermally interpreted as an effective classical description of the finite temperature geometry experienced by quantum fields at a microscopic level. In the macroscopic limit, the averaged contribution of the temperature to the effective geometry is represented by a cosmological constant, which can be interpreted then as a measure of the intrinsic temperature of the vacuum. With this interpretation it seems possible to understand why, on a cosmic scale, the current value of the cosmological constant must be so small, as implied by present observations.