Table of contents

In a theory of gravitation with vector torsion, it is shown that naked singularities could emerge. The result depends on the strength of the coupling constant, and an upper bound on the coupling constant that prevents naked singularities is established.

The authors generalize to p-dimensional extended objects and type II superstrings a recently proposed Green-Schwarz type I superstring action in which the tension T emerges as an integration constant of the equations of motion. The action is spacetime scale-invariant but its equations of motion are equivalent to those of the standard super p-brane for T not=0 and the null super p-brane for T=0. They also show that for p=1 the action can be written in 'Born-Infeld' form.

The interaction of a scalar quantum field with gravity is investigated in the semiclassical context where the spacetime is treated classically. It is essentially understood as a self-interaction of the quantum field, mediated by its own states. The relevant states here are not arbitrary but are selected by the principle of equivalence which is incorporated in the form of specific nonlinear constraint equations. A (state-dependent) dynamics for the quantum field is proposed which is based on a suggested nonlinear field equation.

The authors apply the Melnikov method for identifying chaos in near integrable systems to relativistic particle motion around a Schwarzschild black hole. They start by giving a self-contained introduction to the Melnikov method together with some relevant background on dynamical systems. Then they show that a relativistic particle was unstable circular orbits around a Schwarzschild black hole, and that each one of these gives rise to a homoclinic orbit in phase space, which tends to the unstable one for t to +or- infinity . Finally, the authors use the Melnikov method to conclude that, under most periodic perturbations of the black-hole metric, the homoclinic orbit becomes chaotic.

The gravity waves stress-energy tensor in arbitrary media, on an arbitrary curved background, is derived and studied. The natural low-frequency cut-off is introduced and is shown to depend on the peculiarities of the observer only. The wave equation for weak gravity oscillations is written down with two nonlinear next-after-leading-order terms. The role of nonlinearity is discussed.

A matrix approach is applied to the analytical and numerical investigation of stationary rotationally symmetric solutions in sourceless topologically massive gravity. These solutions are found to be generically spatially compact, with one or two point singularities. Spatially open solutions include, besides previously known solutions, two kinds of asymptotically flat solutions with the wormhole spatial topology.

Constructs exact multicentre static solutions to the pure Chern-Simons limit of vacuum topologically massive gravity and shows that these generate multicentre stationary solutions of the full theory. The corresponding spinless point sources have vanishingly small masses and self-stresses.

The authors consider spacetimes possessing a one-parameter group of isometries with a Killing horizon, N, i.e. an isometry-invariant null hypersurface to which the Killing field is normal. They assume further that the Killing orbits on N are diffeomorphic to R, and that N admits a smooth cross section Sigma , such that each orbit intersects Sigma precisely once. If the surface gravity, kappa , on a generator gamma of N is non-vanishing, then gamma will be null geodesically incomplete. It is proved that any such incomplete generator gamma must terminate in a parallelly propagated curvature singularity whenever the surface gravity has a non-vanishing gradient on gamma . If, however, kappa is constant throughout the horizon, the authors prove that one can extend a neighbourhood of N so that N is a proper subset of a regular bifurcate Killing horizon in the extended spacetime. Since constancy of kappa on N is implied by Einstein's equations and the dominant energy condition, these results indicate that the only physically relevant Killing horizons are bifurcate Killing horizons and horizons with kappa =0. They also prove that for a static or stationary axisymmetric spacetime with a bifurcate Killing horizon, the natural static or stationary axisymmetric hypersurfaces smoothly intersect the bifurcation surface.

Taking into account the gravitational energy, one finds that for an isolated body the inertial mass, active gravitational mass and passive gravitational mass are all equal, so that there is only one mass.