Table of contents

The authors present an algebraic method for solving the field equations of gravitational theories with dynamic torsion.

The late-time behaviour of ( Phi ²) is studied for a massless minimally coupled scalar field in cosmological models with power law expansion. It is shown that ( Phi ²) approaches a constant value at late times if the expansion of the universe is inflationary. An exact solution of the Klein-Gordon equation has been obtained for a two-component universe consisting of dust and radiation. It is found that the state corresponding to the adiabatic vacuum in this case exhibits an infrared divergence at all times.

The authors prove that in the Hartle-Hawking approach to quantum cosmology the existence of an inflationary phase is a general property of minisuperspace models given by a closed Friedmann-Robertson-Walker universe containing a massless scalar field with a lambda phi ⁿ self-interaction. The evolution in time of the cosmic scale factor and of the scalar field in the very early universe is derived, together with the constraints to be satisfied in order to solve the horizon and flatness problems.

Modifications to Einstein's vacuum equations for gravitation in 2+1 dimensions are studied. The addition of the Schouten-Eisenhart 2-forms to the field equations admits gravitational wave solutions although no non-trivial static rotationally symmetric metrics exist. Higher-order derivative models for the metric are discussed together with a 2+1 Brans-Dicke theory. The latter is solved for a static metric exhibiting singularities.

The Frenet-Serret formalism is applied to the study of Killing trajectories in higher dimensions (five and six). The curvature and the higher torsions are expressed in terms of an effective field strength F_ab and their mutual relations established by the use of the Cayley-Hamilton theorem. This is used to show that the surface on which the timelike Killing vector becomes null is a null surface only if the 'rotation' is also null on it.

The timelike Killing vector xi of any static spacetime defines a set of equipotentials on which mod xi mod =constant. The principle that flat spacetimes have zero energy allows a unique expression for the energy, E, within any equipotential. The energy, E, is the energy of the shell of stressed matter on the equipotential that gives the same external metric and a flat interior. The standard Arnowitt-Deser-Misner total energy is retrieved from this expression applied to a large equipotential. The authors compare E with the energy, E_N, obtained from Noether's theorem when the actual spacetime is mapped onto a flat background. The mapping is one in which the timelike Killing fields are identified and the normal congruence of spacelike lines orthogonal to mod xi mod =constant is mapped differentiably on a normal congruence of spacelike lines in the flat background. For a shell it is shown that E=E_N provided the mapping gives zero energy in the flat region. E is given explicitly for axially symmetric fields and the following examples are analysed: spherical symmetry, cylindrical symmetry, the metric of a rod and Lynden-Bell and Pineault's infinite disc of particles in oppositely rotating streams of constant speed. In each example the energy is positive whenever the field is generated by a physical source obeying the weak energy condition. It also increases as the equipotential is made larger.

The authors consider one-soliton perturbations of a flat Friedmann-Robertson-Walker (FRW) cosmological model, with an ideal fluid with pressure equal to energy density (stiff fluid), in the case where the 'pole trajectory' parameter is negative, thereby introducing singularities along certain null hypersurfaces. Starting with a metric that approaches asymptotically the FRW background, they show that it is possible to construct extensions through these hypersurfaces such that the energy-momentum tensor T_mu nu is finite and satisfies the energy conditions. One of the extensions is C^infinity and displays a smooth transformation where the stiff fluid becomes 'tachyonic' (and vice versa), similar to one already discussed by Tabensky and Taub (1973). The other extension is only C¹, providing a sort of 'shock front', with continuity in T_mu nu , that has an associated 'null dust to stiff fluid phase transformation' of the form described by Chandrasekhar and Xanthopoulos (1986).

The problem of non-predictable behaviour of the torsion in the experimentally viable one-parameter teleparallel theory of gravity, first pointed out by Kopczynski (1982), is found to be non-generic, occurring only for very special solutions.

In an accelerated conductor both the inertial forces and the concomitant stress distributions may separately give rise to electric fields. These electric fields manifest themselves as potential differences, as EMF, or as both. This distinction permits the different electric fields to be observed separately. The phenomenological equations of irreversible thermodynamics are extended to include these effects. Through the principle of equivalence, some conclusions may be drawn about the effects of gravitation on conductors. The results of experiments which determine the EMF in ultrasonically accelerated conductors are presented. These results support the phenomenological theory, which predicts that the inertial EMF depend on the free, rather than effective, electron mass.

A theorem of Schoen and Yau (1983) is reformulated to give a condition for trapped surfaces (and hence black holes) expressed in terms of the density and principal pressures of the energy-momentum tensor of matter.

Geometric quantisation is applied to first-class constrained systems. Certain inconsistencies associated with the prequantisation of open gauge algebras and observables in, e.g., the prequantum operator constraint method may be cured at the quantum level by the introduction of suitable polarisations. The limitations of this possibility are discussed. Furthermore it is shown how a large Poisson subalgebra of the ideal of constraint functions can be consistently implemented at the quantum level.

The author gives the solutions for a metric of Weyl's class for sources possessing both inner and outer multipole moments.