Table of contents

We propose a novel BF-type formulation of real four-dimensional gravity, which generalizes previous models. In particular, it allows for an arbitrary Immirzi parameter. We also construct the analogue of the Urbantke metric for this model.

A Lagrangian from which one can derive the third post-Newtonian (3PN) equations of motion of compact binaries (neglecting the radiation reaction damping) is obtained. The 3PN equations of motion were computed previously by Blanchet and Faye in harmonic coordinates. The Lagrangian depends on the harmonic-coordinate positions, velocities and accelerations of the two bodies. At the 3PN order, the appearance of one undetermined physical parameter λ reflects the incompleteness of the point-mass regularization used when deriving the equations of motion. In addition the Lagrangian involves two unphysical (gauge-dependent) constants r'₁ and r'₂ parametrizing some logarithmic terms. The expressions of the ten Noetherian conserved quantities, associated with the invariance of the Lagrangian under the Poincaré group, are computed. By performing an infinitesimal `contact' transformation of the motion, we prove that the 3PN harmonic-coordinate Lagrangian is physically equivalent to the 3PN Arnowitt-Deser-Misner Hamiltonian obtained recently by Damour, Jaranowski and Schäfer.

A generalization of two recently proposed general relativity Hamiltonians, to the case of a general (d + 1)-dimensional dilaton gravity theory in a manifold with a timelike or spacelike outer boundary, is presented.

Conformally invariant quantum field theories develop trace anomalies when defined on curved backgrounds. We study again the problem of identifying all possible trace anomalies in d = 6 by studying the consistency conditions to derive their ten independent solutions. It is known that only four of these solutions represent true anomalies, classified as one type A anomaly, given by the topological Euler density, and three type B anomalies, made up by three independent Weyl invariants. However, we also present the explicit expressions of the remaining six trivial anomalies, namely those that can be obtained by the Weyl variation of local functionals. The knowledge of the latter is in general necessary to disentangle the universal coefficients of the type A and B anomalies from calculations performed on concrete models.

We discuss the higher-dimensional generalization of gravitational instantons by using volume-preserving vector fields. We give special attention to the case of eight dimensions and present a new construction of the Ricci-flat metric with holonomy in Spin(7). An example of the metric is explicitly given. Furthermore, it is shown that our formulation has a natural interpretation in the Chern-Simons theory written by the language of superconnections.

We discuss the construction of perfect fluid stellar objects having optical geometries with multiple necks corresponding to spatially closed unstable lightlike geodesics. We prove that physically reasonable equations of state can give rise to stellar equilibria with arbitrarily many necks. We also show how a first-order phase transition can give rise to quite pronounced secondary necks. The analysis is carried out using a modification of a recent dynamical systems formulation of the TOV equations due to Nilsson and Uggla. Our reformulation allows for a very general family of equations of state including, for example, phase transitions.

In the context of the teleparallel equivalent of general relativity, we obtain the tetrad and the torsion fields of the stationary axisymmetric Kerr spacetime. It is shown that, in the slow rotation and weak-field approximations, the axial-vector torsion plays the role of the gravitomagnetic component of the gravitational field, and is thus responsible for the Lense-Thirring effect.

Higher-derivative terms in the string and M-theory effective actions are strongly constrained by supersymmetry. Using a mixture of techniques, involving both string-amplitude calculations and an analysis of supersymmetry requirements, we determine the supersymmetric completion of the R⁴ action in 11 dimensions to second order in the fermions, in a form compact enough for explicit further calculations. Using these results, we obtain the modifications to the field transformation rules and determine the resulting field-dependent modifications to the coefficients in the supersymmetry algebra. We then make the link to the superspace formulation of the theory and discuss the mechanism by which higher-derivative interactions lead to modifications to the supertorsion constraints. For the particular interactions under discussion we find that no such modifications are induced.

Penrose's identification with warp provides the general framework for constructing the continuous form of impulsive gravitational wave metrics. We present the two-component spinor formalism for the derivation of the full family of impulsive spherical gravitational wave metrics which brings out the power in identification with warp and leads to the simplest derivation of exact solutions. These solutions of the Einstein vacuum field equations are obtained by cutting Minkowski space into two pieces along a null cone and re-identifying them with warp which is given by an arbitrary nonlinear holomorphic transformation. Using two-component spinor techniques we construct a new metric describing an impulsive spherical gravitational wave where the vertex of the null cone lies on a worldline with constant acceleration.

A study of curvature collineations in conformally flat spacetimes is given. It is shown that the only possibilities are (special cases of the) FRW metrics (and their spacelike equivalents), the Bertotti-Robinson metrics and null fluid metrics. The situation is completely resolved in the first two cases and also in the last case when this represents a null Einstein-Maxwell spacetime.

Properties of the horizon mass of hairy black holes are discussed with emphasis on certain subtle and initially unexpected features. A key property suggests that hairy black holes may be regarded as `bound states' of ordinary black holes (without hair) and coloured solitons. This model is then used to predict the qualitative behaviour of the horizon properties of hairy black holes, to provide a physical `explanation' of their instability and to put qualitative constraints on the end-point configurations that result from this instability. The available numerical calculations support these predictions. Furthermore, the physical arguments are robust and should also be applicable in more complicated situations where detailed numerical work is yet to be carried out.

Evolution of electric and magnetic fields in dielectric media, driven by the influence of a strong gravitational wave, is considered for four exactly integrable models. It is shown that the gravitational wave field gives rise to new effects and to singular behaviour in the electromagnetic field.