Table of contents

It is found that the first-order actions for the massless particle and the superparticle have a local translational invariance, which contains the usual reparametrisation invariance. In the case of the superparticle the commutator of two local k supersymmetries closes on this symmetry, just as the global supersymmetry transformations close on rigid translations. It is shown that the bosonic string possesses a similar type of local bosonic symmetry.

The zero tension limit of the classical bosonic string is discussed. The world sheet is a null surface and each point of the string moves independently along a null geodesic.

The asymptotic limit at spatial infinity of Penrose's definition of angular momentum (1982) is considered for asymptotically flat spacetimes containing a nonvanishing stress tensor at i⁰. The discussion complements some recent work of Bizon (1985) and sufficient conditions for angular momentum conservation in the presence of spin-1/2 or 1 massless fields are obtained.

All complex null tetrad transformations are found for which the directions of the tetrad vectors permute rather than mix. A discrete subset for which the vectors themselves are required to permute is of particular interest. Apart from the identity operation and the basic reflection this subset includes the GHP prime operation and left- and right- pseudo-Sachs transformations'. The latter are investigated in detail.

The arrow of time in the Szekeres cosmological models is studied by the use of an invariant depending on the Weyl and Ricci tensors. A vector representing gravitational entropy flux is also introduced. These concepts can be applied satisfactorily to the quasi-spherical models, but their application to the second class of the Szekeres models is somewhat less convincing.

A new definition of angular momentum at future null infinity is proposed which is free of supertranslation ambiguities. A prescription is given to single out a unique Bondi system.

Christodoulou's recent analysis (1984) of naked singularities in time-symmetric Tolman-Bondi collapse is simplified and generalised to a wider class of Tolman-Bondi models. The strengths of the naked singularities are assessed in terms of limiting focusing conditions.

The locally rotationally symmetric Bianchi type-V models possessed of a Cauchy horizon are studied using a tilted comoving basis. The models filled with a perfect fluid having the equation of state of radiation are all shown to have their initial singularity at the same angle of tilt on the fluid curves.

A simple formula for computing the trapping of photons (and other relativistic particles) emitted from the interior of a spherical static configuration is given. Explicit examples of the constant density interior and Tolman's IV solution (1939) are presented.

The authors extend what is known about the structure of (2+1)-dimensional gravitational field theories. The non-existence of any Newtonian limit to these theories is investigated in the presence of Brans-Dicke scalar fields and non-linear curvature terms in the gravitational action. A number of new exact static and non-static solutions of (2+1) general relativity with scalar field, perfect fluid and magnetic field sources are presented and studied in detail. Some of these possess a correspondence with (3+1) solutions of general relativity through a Kaluza-Klein type reduction and exhibit the 'wedge' structure of (3+1)-dimensional solutions describing line sources like vacuum strings. An algebraic classification of (2+1) gravitational fields is derived using the Bach-Weyl tensor. The description of the general cosmological solution is given in terms of arbitrary spatial functions independently specified on a spacelike surface of constant time together with a series approximation to spacetime in the vicinity of a general cosmological singularity.

The authors study Weinberg-type fields, which transform under the (s,0)(+)(0,x) representation of the Lorentz group, in the de Sitter spacetime. They renormalise the vacuum expectation value of the energy-momentum tensor trace using the adiabatic regularisation scheme. They study the relation imposed by the semiclassical Einstein equations among the scalar curvature R and the mass of the fields. Results are explicitly drawn for s=0, 1/2 and 1.

The author calculates the one-loop self-energy in the light-front formulation of gravity. He finds that it is divergent and prescription-dependent.

The author studies a model in between classical relativity and quantum gravity by considering the lowest-order quantum corrections to the classical Einstein-Vlasov equations. He proves that the isotropic solutions of this model are Robertson-Walker universes which are singularity-free, strictly periodic and symmetric for closed universes and which develop a singularity-free, symmetric bounce for open and flat universes.

Non-factorisable solutions of the eleven-dimensional Einstein equations are found. Their internal spaces are SU(3)(X)SU(2)(X)U(1) and SU(3)(X)SO(4) invariant. The conformal factors break these groups, and the ordinary Kaluza-Klein ansatz generates masses to the gauge fields. The approximative procedure is self-consistent, because these gauge fields can be much lighter than the ordinary massive modes, produced by the compactification.

The D=10-E₈*E₈ field theory limit of the heterotic string is compactified on the non-symmetric coset space Sp(4)/SU(2)*U(1) that is known in the limit of decoupled gravity to give three standard fermion generations, with SU(5)*SU(3)_F*U(1)_F as a gauge group in D=4. Allowing for non-vanishing fermion bilinear condensates, and assuming the conventional form of the supersymmetry transformations, the authors prove the presence of a family of N=1 supersymmetric background field configurations. This requires the non-compact space to be flat: (Minkowski)⁴, while the 3-form H_MNP is non-vanishing and proportional to the torsion on the internal manifold. All equations of motion, including that of the dilaton, are satisfied.

The authors present a method for reconstructing a superconnection in the N=3 superspace formulation of the N=4 SYM theory in terms of on-shell physical fields in Minkowski space. This is done through the formulation of N=3 constraint equations in terms of superdifferential forms. In this formulation the constraints imply an overdetermined system of differential equations on anticommuting variables for which the Frobenius consistency conditions are not satisfied globally, but are satisfied only on submanifolds parametrised by solutions of dynamical equations of motion in Minkowski space for the N=4 SYM theory.

Harmonic superspace provides a framework for constructing general hyper-Kahler metrics. The simple example of the Taub-NUT manifold has been given previously. Here it is shown that the harmonic superspace Lagrangian L⁽⁺⁴⁾=¹/₄((D⁺⁺ omega )²-( xi ⁺⁺)² omega ^-2) for a single interacting hypermultiplet describes an N=2 supersymmetric hyper-Kahler sigma model with the d=4 Eguchi-Hanson instanton as its target manifold. The potential omega ^-2 is the unique one invariant with respect to a Pauli-Gursey-like SU(2) group. The authors present other harmonic superspace actions which they expect to yield some other interesting metrics, including the multi-Eguchi-Hanson and Calabi ones, etc.

The authors study Weyl symmetry from a cohomological point of view in theories including gravity in order to determine 0- and 1-cocycles (Weyl invariants and Weyl anomalies). For pedagogical reasons they rederive known results in four dimensions. Then they solve the same problem in six dimensions. The relation of Weyl anomalies to cocycles of the diffeomorphisms are determined: they can be obtained from each other by subtracting a suitable counterterm from the action. Finally it is shown by an example that such a subtraction corresponds to changing the regularisation scheme.

For pt.I see ibid., vol.3, p.233 (1986). In most higher-dimensional theories, the effective matter Lagrangian after compactification is described not only by the radius of the internal space but also by a set of scalar fields (e.g. a dilaton). The author presents stability conditions for (the four-dimensional Friedmann universe (F⁴))*(a constant internal space (K)) in the above class. The stability against non-linear (large) perturbations and the attractor property of the F⁴*K solution are also investigated in order to explain why our universe is the present one. If the local zero minimum of the effective four-dimensional potential U is isolated, the stable F⁴*K solution is always one of the attractors when the 3-space is expanding. In the case that U has a degenerate zero minimum, which appears in theories involving some scale invariance, sufficient conditions for the F⁴*K solution to be the attractor are presented. Both the S² monopole compactification in the six-dimensional, N=2 supergravity theory and the Calabi-Yau compactification in the ten-dimensional, N=1 supergravity theory with or without the gluino condensation SUSY breaking potential are the cases in question. As an example of an isolated zero minimum, the model by Chapline and Gibbons (1984) (a coset compactification in the ten-dimensional, N=1 supergravity theory plus the SUSY breaking mass term) with a cosmological constant is also discussed.

The most general gravity Lagrangian in more than four dimensions is considered which leads to field equations with at most second derivatives of the metric. It consists of a series of dimensionally continued Euler forms and allows spontaneous compactification. The field equations are elaborated for the usual Kaluza-Klein cosmology ansatz and solved in the special case where the extra dimensions form a sphere with constant radius. The dimensional reduction of the theory to four dimensions is discussed as well.

The conformal anomaly for gravitons and coupled gravity-matter excitations is computed in general form for an arbitrary background spacetime. This significantly generalises the previous calculations and allows one to apply them to realistic cosmological backgrounds.

The f-g theory of gravity containing cosmological constants belonging to the weak and strong sector is placed within an effective field theoretical framework. Expressions are derived relating the parameters of the model to the vacuum expectation values of appropriate source terms. The results indicate that there must be cancellations between the many vacuum terms which appear in the theory.

Recently a technique for extending general relativity called algebraic extension was shown to yield only five classes of gravitational theories (general relativity plus four extensions). The particle spectra of these theories are analysed and it is shown that only one of these extensions is ghost free. Two inequivalent theories are shown to result from this extension at the linearised level. One of these is the linearised version of Moffat's theory of gravitation (1979) the other is a new theory which possesses an additional gauge invariance which has been associated with a closed string.

The authors examine in detail the effect of the gravitational field of the Earth and its rotation in the spin precession of neutrons moving in an external steady magnetic field. It is shown that the effect is significant for slow neutrons diffracting in the single crystal and for cold neutrons. Extensive numerical examples are given.

It is shown that a vacuum solution of Einstein's field equations, found by Das (1973) is equivalent to the Kasner solution (1921).