Table of contents

A connection is established between Penrose's (1982) definition of quasi-local mass and the more conventional notions of mass, momentum etc arising from the canonical formalism of general relativity (which exist at least asymptotically). It is shown that each component of the 'angular momentum' twistor can be thought of as the value of a Hamiltonian which generates motions of regions of the spacetime which tend towards one of a collection of 'quasi-Killing vectors' on the bounding 2-surface on which the computations take place. The quasi-Killing vectors are obtained from solutions of the twistor equation, and essential use is made of the spinorial version of the gravitational Hamiltonian first employed in Witten's simplified proof of positive energy in general relativity. These ideas are then used to suggest a variation on Penrose's quasi-local mass definition using 'quasi-conformal Killing vectors' rather than quasi-Killing vectors. This has the advantage that there are only sixteen real quantities rather than the twenty real (ten complex) ones from Penrose's original definition.

The variational theory of an ideal fluid with spin is formulated in Riemannian spacetime within the framework of general relativity theory. It is applied in cosmology, showing the very weak influence of spin on gravity.

The author proves a uniqueness theorem for wormhole spaces with vanishing Ricci scalar. He shows that amongst such metrics and manifolds the unique extremum of the Euclidean action is the Tolman wormhole. He also collects arguments to support the conjecture that this metric is a global minimum in this class.

The contribution of the horizon energy density to black hole temperature is examined. Stable black hole solutions with positive specific heat are shown to exist.

The authors compute the closed spinning-string propagator in coordinate space, in the light-cone gauge, using the first-quantised operator formalism. They find that, as for the case of the bosonic string, the spinning-string propagator may be expressed in terms of elliptic functions. They comment on the covariant generalisation of this light-cone gauge result.

The authors compute explicitly all the Hodge numbers for all Calabi-Yau manifolds realised as complete intersections of hypersurfaces in products of complex projective spaces. This determines the essential part of the matter superfield spectrum for the heterotic superstring compactified on any of these manifolds. They use various techniques presented in the recent literature to obtain 265 distinct Hodge diamonds; they exemplify these techniques, giving all necessary details of their computations.

The relationship between spin structures and superworldsheet topology is shown by the construction of superworldsheets in which the anticommuting coordinates of different coordinate patches are stitched together in non-trivial ways. The four spin structures of the NSR string, corresponding to R-R, NS-NS, NS-R and R-NS boundary conditions are shown to arise as a consequence of topology. More interesting is the existence of more complicated twisted spin structures for the NSR string with N=2 worldsheet supersymmetry. This class of spin structures is also shown to exist for the heterotic string when its heterotic fermions are endowed with a bundle structure. The transformation of spin structures under field redefinitions and modular transformations are examined. Finally the spin structures associated with the ghost sector of the heterotic string are explored.

The author applies Regge calculus to the construction of initial data for Brill waves: axisymmetric nonrotating vacuum solutions of Einstein's equation. The Regge calculus solutions are compared with those of the continuum theory, with encouraging results.

A theorem is given which states that, under certain conditions, local symmetries (isometries, homotheties, affine collineations and conformal motions) can all be extended to global symmetries on spacetime.

Presents the infinitesimal Virasoro symmetry transformation in terms of the generating function in the vacuum which makes it easy to investigate the algebraic structure of the transformation. Extending this formulation into the electrovac fields, one can find a similar symmetry transformation acting in the solution space of the electrovac field equations. Moreover, it is pointed out that these infinitesimal transformations can be exponentiated by using the Riemann-Hilbert transformation.

The integrability conditions for the embedding of a d-dimensional world manifold generated by a (d-1)-dimensional extended object in a flat space are examined. It is shown that, for the case of non-minimal world manifolds with d>2, these conditions contain the Einstein and Yang-Mills equations as an independent set of equations, where the first and third fundamental forms act as gravitation and gauge fields respectively, while the second fundamental form plays the role of the source field. Using these results the string model of relativity is shown to be compatible with general relativity.

Results are presented from a numerical study of spherical GR gravitational collapse using 'observer-time' null slicing. Data on the initial null slice are generated by computing collapse from an initial spacelike slice by means of a standard method and noting parameter values at successive grid points as they are passed by a hypothetical null ray propagating out from the centre. Collapse is then followed to black hole formation using the observer-time code.

An approach toward a self-consistent treatment, at a semiclassical level, of black hole evaporation is presented. The different backreaction effects of massless scalar and vector fields are discussed. On this basis a new evolution scheme for evaporating black holes is suggested in which the evaporation comes to an end before all mass is radiated away.

New and unexpected thermodynamical features of uncharged and non-rotating black holes are discussed starting from a backreaction-corrected temperature expression.

The authors study the gravitational instability of a cosmological model in the presence of a scalar field using the Brans-Dicke theory to describe the gravitational interaction. Using an isotropic distribution function to describe the matter of the universe and assuming a 'de Donder type' gauge condition, they solve the wave equation for the perturbed gravitational field. As in the case of general relativity, the gravitational field is completely classified by its spin and helicity. By using the two-timescales method they solve the perturbed equation for zero helicity waves for the case p=0 and show the time behaviour of the density contrast. Their result shows that the density perturbation grows slightly faster than previously shown by general relativity. This effect is associated with the presence of the scalar field. However, this growth is not explosive.

The author studies the linearised fourth-order field equations for gravitational theories with Lagrangians L=-g(R+1/2aR²+bR_{mu nu} R^{mu nu} )- kappa L_m. He shows that a suitable choice of coordinate conditions involving third derivatives of the potentials leads directly to the general solution of these equations. He states appropriate junction conditions across a timelike (or spacelike) hypersurface of discontinuity. Using these junction conditions, and assuming the metric to be asymptotically flat at spatial infinity, he determines the potentials of an isolated static body in the case 3a+2b<or=0, b>or=0. The new gauge yields the corresponding metric in a spatially isotropic form. These results are applied to a static spherically symmetric body: the potentials are obtained in a simple integral form when the rest-mass density of matter depends upon the distance from the centre. The results previously obtained for a pointlike distribution of matter and for a homogeneous sphere become trivial consequences of the general method.