Table of contents

The characteristic initial-value problem of the gravitational and N-Maxwell plane wave collision is solved exactly.

As a prototype of a type-II superstring compactified on a (2,2) superconformal field theory, the authors give the explicit expression of the SU(3)-invariant reduction of 10D, type-IIA supergravity to D=4 dimensions. It is shown, as expected from general arguments, that this Lagrangian has a standard N=2 supergravity form as dictated by the N=2 tensor calculus.

In this paper the author studies systems of first-order partial differential equations on superspace; by means of a Cauchy-Kowalewsky-like expansion he is able to solve a large class of differential systems.

The author intends to give the correct form of the energy-momentum tensor of an infinite straight superconducting cosmic string in the Minkowski spacetime. Besides the electromagnetic field, they then determine the gravitational field, supposed to be weak, of this source and compare it with an exact metric solution to the Einstein-Maxwell equations, written in the weak-field approximation.

Using the approach of Fradkin and Vasiliev (1987), an action is constructed in 2+1 spacetime dimensions describing interacting massless fields of all integer and half-integer spins s>or=3/2. The action is associated with an infinite-dimensional superalgebra, denoted shs(1, 2)(+)shs(1,2). Truncation to the spin 3/2-spin 2 sector gives the (1,1) type anti-de Sitter (AdS) supergravity theory corresponding to osp(1,2; R)(+)osp(1,2; R). Various properties of the D=3 higher-spin theory, and its relevance to the higher-spin problem in four dimensions, are discussed.

The authors give a prescription for constructing C^infinity solutions of the Einstein-Maxwell constraint equations on R³ which are close to flat initial data and which are exactly vacuum Schwarzschild initial data outside of a compact region. They use a generalisation of a theorem due to Friedrich (1988) to prove that the maximal evolution of these initial data sets are C^infinity -conformally extendible to future and past null and timelike infinity, I⁺, i⁺, I^- and i^-. This establishes the existence of radiating solutions which are smoothly asymptotically flat in both the past and future.

It is shown that the analytical stellar model of Duorah and Ray (1987) does not satisfy Einstein's field equations. All possible solutions derivable from the generalised density distribution are exhibited; these include a solution due to Durgapal and Bannerji. The correct solution following from the ansatz of Duorah and Ray is given. The equation of state for the model is obtained in terms of elementary functions, and the solution is shown to be both regular and physically realistic for a range of masses and radii. A comparison between the model and numerical integrations of neutron stars described by Walecka's relativistic mean-field theory description of neutron matter shows good overall agreement.

The author constructs new solutions of the vacuum Einstein equations which satisfy the colliding wave conditions of Ernst et al. (1988), and which may therefore be interpreted as colliding gravitational plane waves. These solutions have collinear polarisation, and for certain choices of parameters they reduce to previously known solutions.

Rotating mass shells with flat interiors are of interest with respect to the definition of a gravitational field energy density and with respect to the question of relativity of rotation. Previous work on quasispherical rotating mass shells is extended to more general shell shapes. An analysis of the Dirichlet problem for the stationary Einstein equations-which is of considerable interest by itself-shows that for a given non-spherical shell shape in general no mass distribution and no degree of differential rotation on it can realise flatness in the interior. This is explicitly proven in the lowest order of the 'rotation parameter' for mass shells which deviate infinitesimally from a sphere.

The authors consider the Wess-Zumino model in an anti-de Sitter background in the superfield formalism. A partial superconformal invariance of the model is used to treat perturbatively the effects of the background curvature. This turns out to be enough for the purpose of renormalisation and allows them to analyse the possibility of the breakdown of the no-renormalisation theorem to the one-loop order.

Starting from a relativistic Vlasov description for a system of stars that is not 'too relativistic', this paper examines the effects of discreteness fluctuations and shows that, in the limit that these may be associated with relatively proximate stars, the average distribution function f₀ will satisfy the relativistic Landau equation first derived by Israel and Kandrup (1984). This alternative derivation of the Landau equation, which is both simpler and more intuitive, views discreteness effects as being only one particular type of fluctuation which one might envision; and, as such, suggests the possibility of an effective relaxation induced by collective fluctuations, which has already been explored in the Newtonian limit.

Semiclassical approximations, which are useful in the study of a quantum system interacting with a classical system, are studied and compared. A toy quantum mechanical model with two degrees of freedom (which mimics the features of gravity interacting with quantum fields) is used for illustration. In particular, the author considers the Born-Oppenheimer approximation (BOA) (corresponding to G to 0 at fixed h(cross)), the effective action approach (h(cross) to 0 at fixed G) and their combinations. He shows that in the strict BOA limit there is no backreaction on gravity. Gravity is described by classical equations and the fields are quantised in that background. In the effective action approach one can obtain a semiclassical description for gravity, if certain stringent requirements are satisfied. In most situations of interest these conditions will not be met and the O(h(cross)) contribution from gravitons will be comparable to that from quantum fields. He studies the system using both the Schrodinger equation and path integrals and indicates the correspondence.

The author proves a general conformal equivalence between pairs of Lagrangians (L(R); L(R)) and applies it to the pair (R^m; R^m) with m=(3m-4)/(2m-3).

It is demonstrated how classical properties of the intrinsic time variable in minisuperspace of quantum gravity would emerge in the sense of a continuous measurement process solely through interaction with fermionic degrees of freedom. This measurement is much less effective than that by bosons considered in a previous paper. Continuous measurement by fermions would not lead to classical properties for values of intrinsic time near the singularity of a Friedmann universe. It is argued that this result remains true for the full quantum theory of gravity.