Table of contents

The equations governing potentials for generating perturbations of algebraically special Einstein-Maxwell spacetimes are written in the spin coefficient formalism. For type-D spacetimes the perturbations in all directional derivatives, spin coefficients and curvature components are written in terms of the potentials and their derivatives.

The authors give a prescription for the application of the inverse scattering generation technique of Belinskii and Zakharov (1978,1979) to perfect fluid cosmological seed solutions in the context of a five-dimensional Kaluza-Klein formalism. As an example they present a two-soliton metric generated from a Friedmann-Robertson-Walker background with a perfect fluid which follows a general gamma-law equation of state. The resulting solution becomes asymptotically the background for large times.

A definition of quasi-local momentum is given. It is shown that, in the absence of matter, the leading term is determined by the Bel-Robinson tensor.

The author finds an exact solution of the Einstein-Maxwell equations which represent a charged black hole, the charge being equal to the mass, and an infinite cosmic string in equilibrium.

Recent developments in higher-dimensional unified field theories have led to a great deal of interest in compact spaces admitting Einstein metrics. Almost all the physics literature on such spaces has been concerned with the very atypical case in which the space is homogeneous. The authors present a very simple construction of a wide class of inhomogeneous compact Einstein spaces with positive Ricci curvature found earlier by Berard-Bergery, (1982) which arise as certain 2-sphere bundles over an arbitrary Einstein-Kahler base space of positive Ricci curvature. Solutions on complete non-compact manifolds also exist, with negative or zero Ricci curvature.

It is shown that there exists a correspondence between the theories of Jordan algebras and Freudenthal triple systems with classical particles and classical bosonic strings, respectively. In the latter case one is forced to consider the string embedded in a (D+2)-dimensional spacetime with two times and D spaces. The usual string is recovered upon imposing additional constraints on the (D+2) Virasoro algebra.

A new formulation of the superparticles in light-cone harmonic superspace is presented. The local fermionic invariance is shown to be generated by the conditions for light-cone analyticity. In a special gauge this invariance is reduced to ordinary supersymmetry and the physical variables of the superparticle become the coordinates of the analytic subspace. The Dirac method of quantisation is applied to take into account the kinematical constraints on the coordinates. The coupling to a super-Yang-Mills background and its implications for the gauge algebra are discussed.

Using the canonical Hamiltonian for vierbein general relativity, the ten primary constraints are shown to lead to four secondary constraints. The algebra of these constraints is found and is consistent with the constraint algebras previously known.

The authors investigate the propagation of small-amplitude gravitational waves through pressureless matter ('dust'). After establishing the local linearisation stability of Einstein's equation for dust about any of its solutions they use the WKB method to study the locally plane, linearised perturbations of an arbitrary background dust spacetime asymptotically for small wavelengths. The dispersion relation exhibits two modes. One is simply degenerate and represents gravitational waves, whereas the other is doubly degenerate and describes density and vorticity perturbations. The waves are shown to propagate along the null geodesics of the background; in leading WKB order their amplitudes behave as in vacuo. The rays associated with the matter mode are the wordlines of the background dust. In leading order the perturbations of density and 4-velocity vanish for both modes.

The authors derive an expression for the singular part of the stress-energy tensor on a hypersurface in spacetime in terms of the discontinuities in fundamental forms associated with the surface for both the non-null case, where the results are standard, and the null case. They then derive the minimum conditions which must be satisfied in order to glue two spacetimes together along such a hypersurface. In both cases, the essential requirement is only that the naturally induced (possibly degenerate) 3-metrics on the hypersurface must agree.

A marginal 2-surface is, by definition, covered by a 2-surface admitting a nowhere-zero null normal field of zero expansion. A complete marginal 2-surface which is either compact, or non-compact and subject to certain asymptotic geometric constraints, is said to be well tempered. A well tempered marginal 2-surface admitting a nowhere-timelike variation through well tempered marginal 2-surfaces is said to be stable. In a spacetime satisfying the dominant energy condition, a stable well tempered marginal 2-surface is homeomorphic to S², P², R², T², S*R a Klein bottle or a Mobius band. Only the topologies S², P² and R² may be compatible with genericity conditions. Of stable compact embedded marginal 2-surfaces which are bounding in a spacelike hypersurface, those homeomorphic to P² occur in pairs, as do those homeomorphic to a Klein bottle. Stable compact embedded marginal 2-surfaces which are achronal and develop from data on a simply connected partial Cauchy surface are homeomorphic to S² or T².

The reduction of the gauge symmetry from the group G=SO(4,1) to the subgroup H=SO(3,1) is investigated in detail in a gauge theory based on the (4,1) de Sitter group, and the relation to the Lorentz gauge symmetry appearing in a vierbein formulation of gravity is pointed out. A key concept in this context is that of soldering and the related interlocked nature of the de Sitter frame bundle over spacetime with the ordinary Lorentz frame bundle over spacetime considered in a general relativistic framework. Generalised spinor fields Psi are introduced which transform under the non-linear realisation of G on the stability subgroup H of the origin in G/H, i.e. under the so-called SO(4,1)-Wigner rotations. The appearance of effects related to torsion in the dynamical equation for Psi is pointed out. The virtue of the present approach compared to the previous direct product formalism is that here the same spinor degrees of freedom transform, because of soldering, under both the internal de Sitter group and the spacetime Lorentz group.

Using a recently developed schema of Isham and Kuchar (1985) a canonical representation of spacetime diffeomorphisms is found for parametrised Maxwell electrodynamics. Gauge invariance hampers the direct application of the schema because the scalar potential phi _{perpendicular to} plays the role of a Lagrange multiplier which enforces the Gauss constraint and therefore lies outside the extended phase space. This difficulty is circumvented by turning the scalar potential into a canonical momentum pi conjugate to a supplementary scalar field psi and prescribing their dynamics by imposing the Lorentz gauge conditions. The super-Hamiltonian and supermomentum of this modified theory satisfy the Dirac closure relations and induce the correct behaviour of field projections under hypersurface shifts and tilts. These properties lead to the canonical representation of the generators of spacetime diffeomorphisms. The Maxwell theory is recovered at the end by imposing two additional constraints, the C(x):= psi (x)=0 constraint and the Gauss constraint, each of which is preserved by the generators of spacetime diffeomorphisms. The situation is compared with that arising in canonical geometrodynamics.

Much recent work on higher-dimensional field theories is based on the assumption that the universe (or its ground state) may be represented as a product M₄*N, where N is a compact Riemannian manifold. The author argues that, just as it is necessary to justify the assumption of compactness by means of a physical mechanism (spontaneous compactification), so also does one need to explain the splitting between internal and external spaces. Various possible mathematical interpretations of the splitting are discussed, as well as some results which may be relevant to the solution of the 'splitting problem'.

Standard work on geodesic focusing assumes that a pointwise inequality, known as an energy condition, holds. This pointwise condition has been weakened by Tipler (1978) to the requirement that a certain integral comes out to be non-negative for large enough parameter intervals. In this paper, this integral condition is further weakened to cover cases where the integral of interest is only periodically non-negative. Thus, some situations where there are repeated violations of the energy conditions are shown to still lead to the focusing of geodesics, despite these violations. Focusing effects are discussed both for full as well as half geodesics. The existence of singularities in situations where the energy conditions are violated, as in inflationary cosmological models, is also discussed.

In a gauge theory the topological structure of the group of gauge transformations G can have important consequences. Information is obtained about the topology of G in four dimensions and this is used to study the existence of a global gauge fixing condition. The topologies nature of G also allows inequivalent topological sectors to exist and these are discussed in four- and five-dimensional gauge theories. Finally, the topological structure of G imposes constraints on the existence of global anomalies in four-dimensional gauge theories.

This paper develops a new approach to Regge calculus, a numerical technique used for the calculation of general relativistic spacetimes. The method is developed in an original '3+1' form in such a way that it can be applied to inhomogeneous spacetimes. In a second paper the method will be tested by application to spherically symmetric vacuum spacetimes.

For pt.I see ibid., vol.4, p.375 (1987). In paper I an original '3+1' form of Regge calculus was developed. In the current paper the method is tested by application to spherically symmetric vacuum spacetimes. Three different time slicing conditions are used and, where appropriate, the results are compared with the analytic solution with encouraging results.

The author investigates the 'space'+'time' canonical decomposition of (N=1, flat) Minkowski superspace and discuss its applications in the identification of the canonical superfield variables of superspace field theories. In order to obtain a kinematical (i.e. not involving time shifts) subclass of the full Minkowski supersymmetry it becomes necessary to consider a type of Complex extension of the usual or Real superspace which, without disrupting the basic component field structure of superfields, naturally enlarges the class of superPoincare symmetries in an essential way. The methods developed are applied to the simple superspace theories of (free) chiral and Abelian vector supermultiplets.

The author obtains the radial decoupled Dirac equation in the NUT-Kerr-Newman spacetime and then study the Hawking thermal spectrum near the horizon of the metric.

This paper considers a new system of linear equations whose solution describes a hierarchy of determinant solutions to the stationary axially symmetric Einstein equations in general relativity.

A method of constructing reducible supergravity multiplets from other super-gravity multiplets is described. The method is to expand the reducible multiplet's covariant derivatives in terms of another multiplet's covariant derivatives, Lorentz group generators and charge operators, using superfield expansion coefficients. A sketch of the construction of the '16+16' multiplet from the 'minimal 12+12' and '4+4' multiplets is used as an example. Also included are the solutions for the Bianchi identities for the 'minimal 12+12' and the 'new minimal 12+12' multiplets. This exhibits their superfield content and corrects a previously published result (Gates et al. 1983).

The anomalous chiral Ward identity for the gauge fields in a class of realistic Kaluza-Klein models is obtained. Particular attention is paid to the six-dimensional model of Randjbar-Daemi et al (1983), including Pauli couplings and the reduction of appropriate topological terms.

The author shows that within the non-linear electrodynamics of Born-Infeld type coupled with gravitational fields admitting a non-null Killing vector, there exists complex potentials xi and phi , which generalise the well known gravitational and electromagnetic Ernst potentials of the Einstein-Maxwell theory. The corresponding Lagrangian and reduced set of equations referred to a three-dimensional metric are given.

A description of a charged massive Proca field in a background Riemann-Cartan spacetime is discussed, Investigation of the WKB limit of the Proca field equations coupled to Riemann-Cartan gravity leads to the equations of motion of a 'Proca test particle'. The definition of a classical parameter related to the spin polarisation of the WKB limit of a particle is discussed. It is shown here that the spin polarisation of a Proca test particle precesses with a velocity linked only to axial and tensor irreducible parts of the torsion of the spacetime where this particle is immersed.

It is shown that, if the local gauge symmetry of general relativity is broken, the singularity theorems may be evaded, and in particular the cosmological singularity of the standard model may be prevented, even if the gravitational sources satisfy the strong energy condition.