Table of contents

Spacetimes generated by a lightlike particle source for topologically massive gravity and its limits-Einstein gravity and the pure gravitational Chern-Simons model-are obtained both by solving the field equations and by infinite boosts of static metrics. The resulting geometries are the first known solutions of topologically massive gravity that are asymptotically flat and generated by compact matter sources. Explicit metrics describing various multiphoton solutions are also derived. For Einstein gravity, the authors also construct such solutions by null boost identifications of Minkowski space and thereby obtain limits on the energies of the sources.

The distinction between three- and four-dimensional spacetimes is considered with particular reference to possible changes of spatial topology; implications for three-dimensional models of quantum gravity are discussed. The situation in which the metric may be kinked is also investigated. Finally, the case of topology change in two spacetime dimensions is discussed briefly.

The author presents a new family of stationary and axisymmetric perfect-fluid solutions. The metrics are defined by the solutions to a system of two coupled ordinary differential equations of second order on three unknown functions. Therefore, they depend on an arbitrary function of one coordinate. The fluid has, in general, differential rotation. The equation of state is rho = rho +const. Some properties of the solutions are described and an explicit example given in terms of elementary functions is presented.

Two previously known wormholes arising from a conformally coupled ( xi =1/6) scalar field and a minimally coupled imaginary scalar field are also found to allow wormholes for various couplings xi . Quantum versions of such wormholes are expected to occur but only for the same values of xi as required in the classical case.

The author considers first a classical particle whose action depends not only on the pathlength of the trajectory of the particle, but also on its curvature. The m to 0 limit (namely, the massless limit when there is no dependence on the curvature) is attained through introduction of an auxiliary 'einbein' field e. A supersymmetric extension is then considered. The resulting action is reparametrization invariant and supersymmetric, but does not have the local fermionic kappa -invariance which is present in the limiting case when dependence on the curvature vanishes. Dependence of the action on the acceleration is eliminated through introduction of further auxiliary fields, allowing one to quantize using the Dirac constraint formalism.

A relationship between the geometry of the (4 mod 4)-dimensional superspace of N=1 supergravity, M, and the holomorphic structure of the (5 mod 2)-dimensional superspace of null supergeodesics, N, associated with M is investigated. An invariant definition of the local supertwistor bundle T on M is found, and it is proved that its dual graded skew square Lambda ²T^* admits a non-zero horizontal section if and only if M is superconformally Einstein. A supersymmetric extension of LeBrun's Einstein bundle (1989) on N is constructed. The significance of this bundle stems from the fact that its non-vanishing holomorphic sections are in one-to-one correspondence with solutions of N=1, D=4 supergravity equations with cosmological constant. All these constructions are investigated in more detail in the category of self-dual superspaces of N=1 supergravity, and a supersymmetric generalization of Penrose's nonlinear graviton construction (1976) is obtained.

The question of the existence of Galilean invariant actions for extended objects is studied, in particular when they are effective descriptions for topological defects. It is concluded that, although there is no problem in constructing a Galilean invariant action for particles, the answer is negative for higher dimensional objects, under certain reasonable assumptions. It is concluded that non-relativistic extended objects are necessarily strongly coupled to some background.

The scattering of test particles by a global monopole represented by a spacetime with a solid deficit angle is studied. It is found that the geodesics are equivalent to those of a particle in 2+1 dimensions. For quantum scattering a partial wave analysis is made to obtain analytic expressions for the phase shifts scattering amplitudes, cross sections and the total wavefunction. The results are compared with the analogous study for local cosmic strings and with the S-matrix obtained when both topological defects travel at ultra-relativistic speeds.

Within the framework of the quantum field theory at finite temperature, the author determines the Euclidean thermal Green function for a massless scalar field in a conical spacetime. This result enables one to evaluate in integral form the mean-square field as a function of the temperature. The author is also able to calculate in the high-temperature limit the thermal average of the energy-momentum tensor for a conformal scalar field.

The authors construct an infinite-dimensional family of solutions to Einstein's field equations representing collisions between plane gravitational waves with variable polarization. The boundary conditions on the null hypersurfaces are studied and presented as a set of algebraic conditions for the constant coefficients of the Legendre functions. The behaviour of the gravitational field near the focusing two-surface is also analysed and some of the issues related to the strong cosmic censorship conjecture are briefly discussed.

The authors present new results on the recently described 'time shift' phenomena in the nonlinear (self) interaction of cylindrical solitonic electro-gravitational waves, as they are reflected off the symmetry axis. Central to the analysis is the construction of an appropriate descriptive framework in general relativity, given by the introduction of the notion of a 'test' soliton, within which one can give an invariant meaning to concepts such as 'localized perturbations' and their corresponding 'time shifts'.

The author calculates the quasi-local mass contained in various types of sphere for two new definitions of quasi-local momentum. He compares his results with those obtained for other definitions in the literature.

The authors present in a concise analytical form two asymptotically flat metrics describing the superposition of the Kerr solution with an arbitrary static vacuum Weyl field which differ in their angular momentum distributions. They are then used for the construction of two asymptotically flat generalizations of the Kerr-Newman spacetime possessing the full set of mass-multipole moments able to describe the exterior gravitational field of a charged rotating arbitrary axisymmetric mass.

Coordinate-free representations of the Riemann and Einstein tensors are obtained, and approximate diffeomorphism invariance is shown to exist for near-flat simplicial geometries with sufficiently fat triangulations. Then, by finding the analogues of the contracted Bianchi identities for these near-flat geometries, interdependence of the Regge equations is shown, and the relation to the coordinate degrees of freedom of the continuum is discussed.

A spinor particle is considered in the background gravitational field due to a tubular matter source with axial interior magnetic field and vanishing exterior magnetic field. In the locally flat spacetime around this tubular matter source the authors study the gravitational analogue of Aharonov-Bohm effect for this particle. They also look at the motion of light rays and they discuss the existence of a self-force on an electric charge at rest in this background.

The author characterizes those boost symmetric spacetimes which, in addition to de Sitter space, admit spatially compact, (locally) conformally flat, time symmetric Cauchy hypersurfaces and satisfy Einstein's vacuum field equations with a cosmological constant. The Cauchy surfaces all turn out to be (finite quotients of) Riemannian products and warped products of (S¹,dy²) with (S², gamma _k) where gamma _k is the canonical metric of constant positive sectional curvature k.

The author describes a differential geometric unification and reformulation of earlier pseudotensorial approaches. It is shown that, along coordinate sections, the pull backs of the contravariant and dual forms of Sparling's form, defined on the bundle of linear frames L(M) over the m-dimensional spacetime M, are the Bergmann and the Landau-Lifshitz pseudotensors, respectively. Although the pull backs of Sparling's form along rigid sections are not exactly the energy-momentum tensors of the rigid basis description of gravity, they are always tensorial and the pull backs of the full Sparling equation are always the equations expressing the canonical (pseudo) tensors by the corresponding superpotentials. For any vector field on the spacetime an (m-1) form, called the Noether form, is defined on L(M) whose pull backs to the spacetime are, however, always the corresponding canonical Noether (pseudo) currents.