Table of contents

A solution is presented which describes the collision of gravitational waves in a closed Friedmann--Robertson--Walker background. The matter field present is taken to be that of a stiff perfect fluid. It is shown that, unlike the situations in which the background is open or spatially flat, the solution in this case contains a future space-like curvature singularity.

New exact solutions of Einstein's gravity coupled to a self-interacting conformal scalar field are derived in this work. Our approach extends a solution-generating technique originally introduced by Bekenstein for massless conformal scalar fields. Solutions are obtained for a Friedmann--Robertson--Walker geometry both for the cases of zero and non-zero curvatures, and a variety of interesting features are found. It is shown that one class of solutions tends asymptotically to a power-law inflationary behaviour with p>1, while another class exhibits a late time approach to the behaviour of the coasting models. Bouncing models are also obtained. A general discussion of the asymptotic behaviour and of the possibility of occurrence of inflation is provided.

We study the cohomology of the critical string using the BRST charge in a special basis in which it contains three separately nilpotent BRST charges. This allows us to obtain the physical operators in three steps. In the first step we obtain the cohomology associated to a spin-4 constraint only, and it contains operators of the minimal model. In the next step, where the spin-3 constraint is added, these operators get dressed to operators of the Virasoro minimal model. Finally, the Virasoro constraint is added to obtain the cohomology of the critical string. We describe the structure of the complete cohomology and compare with other results.

We consider the specialization to spatially homogenous solutions of the Jacobson formulation of N=1 canonical supergravity in terms of Ashtekar's new variables. We find that the classical Poisson algebra of the supersymmetry constraints is preserved by this specialization only for Bianchi type A models. The quantization of supersymmetric Bianchi type A models is carried out in the triad representation. We find the physical states of this quantum theory. Since we are missing a suitable inner product on these physical states, our results are only formal.

Spacetime discretized in simplexes, as proposed in the pioneer work of Regge, is described in terms of self-dual variables. In particular, we elucidate the `kinematic' structure of the initial value problem, in which 3-space is divided into flat tetrahedra, paying particular attention to the role played by the reality condition for the Ashtekar variables. An attempt is made to write down the vector and scalar constraints of the theory in a simple and potentially useful way.

The propagation of quantum fields in bundles associated with Poincaré frame bundles over curved spacetime is formulated in terms of path integrals that conform to the strong equivalence principle of general relativity. This propagation is based on quantum connections that arise from the Levi-Civita connection form, and is locally governed by energy density operators that arise from well defined stress--energy tensor operators. The existence of a Poincaré gauge invariant and locally conserved probability current and of action integrals is established as a basis for its physical interpretation. Its relation to the conventional S-matrix perturbation series is studied in the special relativistic regime.

We present a compactified version of the three-dimensional black hole recently found by considering extra identifications and determine the analytical continuation of the solution beyond its coordinate singularity by extending the identifications to the extended region of the spacetime. In the extended region of the spacetime, we find a topology change and non-trivial closed time-like curves both in the ordinary three-dimensional black hole and in the compactified one. Especially, in the case of the compactified three-dimensional black hole, we show an example of topology change from one double torus to eight spheres with three punctures.

There is an exact solution of Einstein's equations corresponding to a particle emitting null fluid anisotropically, and accelerating because of the recoil. I examine this solution and find no sign of emission of gravitational radiation. I give the Killing vectors of the metric, and some of the curvature invariants.

For an arbitrary equation of state giving the pressure P as a function of the energy density , it is shown that the perfect fluid model defined thereby (and also the corresponding Ginzburg--Landau type generalization) can be represented by a variational theory in which the independent fields are an antisymmetric Kalb--Ramond gauge form, , a pair of scalar vorticity gauge potentials, , and a dilatonic scalar amplitude . The associated physical fields consist of the dilatonic ampitude itself, together with an axionic field, , and a vorticity field, . The Lagrangian for the perfect fluid case will be given by for a dilatonic self-coupling potential V whose form as a function of depends on the equation of state in such a way that its on-shell value will be given by .

Zeta-function regularization is applied to the evaluation of the one-loop effective potential for SO(10) grand unified theories in de Sitter cosmologies. When the Higgs scalar field belongs to the 210-dimensional irreducible representation of SO(10), attention is focused on the mass matrix relevant for the symmetry-breaking direction, to agree with the low-energy phenomenology of the standard model of particle physics. The analysis is restricted to those values of the tree-level potential parameters for which the absolute minimum of the classical potential has been evaluated. As shown in the recent literature, such minima turn out to be or invariant. Electroweak phenomenology is more naturally derived, however, from the former minima. Hence the values of the parameters leading to the alternative set of minima have been discarded. Within this framework, the flat-space limit and the general form of the one-loop effective potential are studied in detail by using analytic and numerical methods. It turns out that, as far as the absolute-minimum direction is concerned, the flat-space limit of the one-loop calculation with a de Sitter background does not change the results previously obtained in the literature, where the tree-level potential in flat spacetime was studied. Moreover, even when curvature effects are no longer negligible in the one-loop potential, it is found that the early universe can only reach the absolute minimum.

General relativistic anisotropic fluid models whose fluid flow lines form a shear-free, irrotational, geodesic timelike congruence are examined. These models are of Petrov type D, and are assumed to have zero heat flux and an anisotropic stress tensor that possesses two distinct non-zero eigenvalues. Some general results concerning the form of the metric and the stress tensor for these models are established. Furthermore, if the energy density and the isotropic pressure, as measured by a co-moving observer, satisfy an equation of state of the form , with , then these spacetimes admit a foliation by spacelike hypersurfaces of constant Ricci scalar. In addition, models for which both the energy density and the anisotropic pressures only depend on time are investigated; both spatially homogeneous and spatially inhomogeneous models are found. A classification of these models is undertaken. Also, a particular class of anisotropic fluid models which are simple generalizations of the homogeneous isotropic cosmological models is studied.

The Abbott--Deser (AD) mass in asymptotically de Sitter spacetime is a conserved Killing `energy'. We show that the AD mass can be negative in some situations but may still deserve the title of `gravitational mass'. In order to see the property of negative AD mass we consider the Tolman--Bondi dust sphere solution. The negative AD mass prevents the dust sphere's gravitational collapse. Rather it causes cosmic expansion, resulting in isotropic and homogeneous de Sitter spacetime locally. As a result, the cosmic no hair conjecture holds even though the AD mass may be negative.

New perfect-fluid solutions of Einstein's field equations have been found by means of the generalized Kerr--Schild transformation for perfect-fluid metrics. All these solutions are Petrov type D with the velocity vector of the fluid out of the two-space spanned by the two null principal directions of the Weyl tensor. In general, the solutions have just one Killing vector, but some special cases admit two commuting Killing vectors. All the solutions can be interpreted as inhomogeneous cosmological models, and an interesting property is that they contain some Friedman--Robertson--Walker metrics as special cases. Thus, they can be seen as inhomogeneous generalizations of the standard FRW cosmologies.

The coupled system of the Einstein--Maxwell perfect fluid equations is under study. Two new families of exact solutions are submitted. One of them contains as a particular case a new general solution for Lorentz force-free stationary charged dust in rigid rotation. Generation of new solutions is possible due to a relative freedom in choosing the electromagnetic 4-potential. A number of known solutions are derived as particular cases. Some properties of the fluid and the electromagnetic field are presented.

Gravitational wave coincidence experiments between bars and interferometers may be an attractive option once the new generation of full scale interferometers begins taking data. We discuss various ways in which these disparate types of data can be compared in searches for bursts (from supernovae, for example), for pulsar signals, and for a stochastic background. Comparison of broadband interferometer data with narrowband bar data is appropriate in most searches for bursts, but in many cases the results---especially null results (upper limits)---are difficult to interpret. By narrowbanding the interferometer data to the bandwidth of the bar detector, one produces data sets that may give much clearer information in certain burst searches and that are appropriate for searches for a stochastic background of gravitational waves. We suggest, in fact, that there are circumstances where searches for a stochastic background could be more efficiently performed between a bar and an interferometer than between two interferometers. We examine, in some detail, the effect of narrowbanding the interferometer data. We apply this method to a real interferometer and bar data and assess its signal-to-noise performance for different classes of gravitational wave signals.

We investigate the equality of inertial and gravitational mass in a wide class of scalar--tensor theories. We derive a general expression for the active mass (gravitational mass) and the inertial mass related by a term which can be seen as the energy of the scalar field. We discuss a generalization of the Tolman expression for the energy, the binding energy, and the virial theorem.

We introduce the linear connection in the non-commutative geometry model of the product of continuous manifold and the discrete space of two points. We discuss its metric properties, define the metric connection and calculate the curvature. We define also the Ricci tensor and the scalar curvature. We find that the latter differs from the standard scalar curvature of the manifold by a term, which might be interpreted as the cosmological constant, and apart from that we find no other dynamic fields in the model. Finally we discuss an example solution of flat linear connection, with the non-trivial scaling dependence of the metric tensor on the discrete variable. We interpret the obtained solution as confirmed by the standard model, with the scaling factor corresponding to the Weinberg angle.

A recent paper has considered the renormalization of conformally invariant theory on a background spacetime of constant curvature to third order in the coupling . It was claimed that to this order a wavefunction renormalization is required that has a term involving the Euler constant . We re-calculate the diagrams that contribute to the renormalization of the two-point function and find that no such term is necessary, and that the term quoted in the previous work is incorrect. Some numerical errors of the previous work are also corrected. The general conclusions of the previous work are not affected.

The solution recently published by Haggag and Hajj-Boutros is not new.