Table of contents

We consider linearized 5-d gravity in the Randall-Sundrum brane world. The class of static solutions for linearized Einstein equations is found. We also we obtain wave solutions describing radiation from an imaginary point source located at the Planck distance from the brane. We analyse the fields' asymptotic behaviour and peculiarities of matter sources.

Previous work in the literature has studied gravitational radiation in black hole collisions at the speed of light. In particular, it had been proved that the perturbative field equations may all be reduced to equations in only two independent variables, by virtue of a conformal symmetry at each order in perturbation theory. The Green function for the perturbative field equations is analysed here by studying the corresponding second-order hyperbolic operator with variable coefficients, instead of using the reduction method from the retarded flat-space Green function in four dimensions. After reduction to canonical form of this hyperbolic operator, the integral representation of the solution in terms of the Riemann function is obtained. The Riemann function solves a characteristic initial-value problem for which analytic formulae leading to the numerical solution are derived.

Two spacetime metrics are constructed that provide examples that were conjectured to exist in a recent paper by Hall and Lonie. The first metric is an Einstein space that has a null recurrent vector field. The second metric is conformally flat and also has a null recurrent vector field.

The gravitational lensing due to an axially symmetric lens with a minimally coupled scalar field is considered. Comparison is made with the case of a spherically symmetric lens analysed previously in the literature, and a different dependence of the image positions on the `scalar charge' is found. In particular, while the formation of four images, two Einstein rings and one radial critical curve (RCC) is possible for different configurations with both types of lenses, their positions are different from one metric to the other. Nevertheless, these differences are very small and, even if such configurations are ever observed, it seems to be very difficult to distinguish between the spacetimes studied here.

In this paper we outline a rather general construction of diffeomorphism covariant coherent states for quantum gauge theories. By this we mean states ψ_(A,E), labelled by a point (A,E) in the classical phase space, consisting of canonically conjugate pairs of connections A and electric fields E, respectively, such that: (a) they are eigenstates of a corresponding annihilation operator which is a generalization of A-iE smeared in a suitable way; (b) normal ordered polynomials of generalized annihilation and creation operators have the correct expectation value; (c) they saturate the Heisenberg uncertainty bound for the fluctuations of Â,Ê; and (d) they do not use any background structure for their definition, that is, they are diffeomorphism covariant.

This is the first paper in a series of articles entitled `Gauge field theory coherent states (GCS)' which aims to connect non-perturbative quantum general relativity with the low-energy physics of the standard model. In particular, coherent states enable us for the first time to take into account quantum metrics which are excited everywhere in an asymptotically flat spacetime manifold as is needed for semiclassical considerations.

The formalism introduced in this paper is immediately applicable also to lattice gauge theory in the presence of a (Minkowski) background structure on a possibly infinite lattice.

We consider a family of cylindrical spacetimes endowed with angular momentum that are solutions to the vacuum Einstein equations outside the symmetry axis. This family was recently obtained by performing a complete gauge fixing adapted to cylindrical symmetry. In this paper, we find boundary conditions that ensure that the metric arising from this gauge fixing is well defined and that the resulting reduced system has a consistent Hamiltonian dynamics. These boundary conditions must be imposed both on the symmetry axis and in the region far from the axis at spacelike infinity. Employing such conditions, we determine the asymptotic behaviour of the metric close to and far from the axis. In each of these regions, the approximate metric describes a conical geometry with a time dislocation. In particular, around the symmetry axis the effect of the singularity consists in inducing a constant deficit angle and a timelike helical structure. Based on these results and on the fact that the degrees of freedom in our family of metrics coincide with those of cylindrical vacuum gravity, we argue that the analysed set of spacetimes represent cylindrical gravitational waves surrounding a spinning cosmic string. For any of these spacetimes, a prediction of our analysis is that the wave content increases the deficit angle at spatial infinity with respect to that detected around the axis.

The generalized scalar-tensor (GST) theory is modified. In the modified GST theory, the cosmological term Λ is a function of the scalar field ϕ and of its time derivative {}² as well. We obtain exact solutions for the scale factor, the scalar field and the cosmological term which evolves with a different dependence on time for each era of the universe. The cosmological `constant' and flatness problems are examined in the simple case of a flat universe.

The Casimir energy for the massless scalar field of two parallel conductors in a two-dimensional Schwarzschild black hole background with Dirichlet boundary conditions is calculated by making use of general properties of the renormalized stress tensor. We show that the vacuum expectation value of the stress tensor can be obtained from the Casimir effect, the trace anomaly and Hawking radiation.

We construct exact static, axisymmetric solutions of Einstein-Maxwell-dilaton gravity presenting distorted charged dilaton black holes. The thermodynamics of such distorted black holes is also discussed.

We show explicitly that in (2 + 1) dimensions the general solution of the Einstein equations with negative cosmological constant on a neighbourhood of timelike spatial infinity can be obtained from BTZ metrics by coordinate transformations corresponding geometrically to deformations of their spatial infinity surface. Thus, whatever the topology and geometry of the bulk, the metric on the timelike extremities is BTZ.

Using a recently developed perturbation formalism based on curvature quantities, we investigate the linear stability of black holes and solitons with Yang-Mills hair and a negative cosmological constant. We show that those solutions which have no linear instabilities under odd- and even-parity spherically symmetric perturbations remain stable under odd-parity, linear, non-spherically symmetric perturbations.

We report on solutions to the Einstein field equations representing spherically symmetric, shear-free spacetimes with heat flux. The source matter for all of these spacetimes satisfies an equation of state of the barotropic form p = αρ where p and ρ are the pressure and density of the matter fluid while α is a constant. As an application, we model the collapse of a shear-free, radiating star which dissipates energy in the form of a radial heat flux. The heat flows from the hotter parts of the centre to the overlying cooler parts. The density, the pressure and the heat flux all decrease as we move towards the boundary of this star. An interesting aspect of our solutions is that we can describe the formation of a semi-stable stellar configuration using our general relativistic solutions.

We discuss the five-dimensional axisymmetric metric with non-zero parameter η, the field equation is reduced to the Ernst equation with η and the Laplace equation. For η = 1, the corresponding solution describes the five-dimensional axisymmetric spacetime with an electrostatic field. We find that the TS solutions can be generalized to those with arbitrary non-zero η.

In this paper we study brane-world scenarios with a bulk scalar field, using a covariant formalism to obtain a four-dimensional Einstein equation via projection onto the brane. We discuss, in detail, the effects of the bulk on the brane and how the scalar field contributes to the gravitational effects. We also discuss the choice of conformal frame and show that the frame selected by the induced metric provides a natural choice. We demonstrate our formalism by applying it to cosmological scenarios of Randall-Sundrum- and Horava-Witten-type models. Finally, we consider the cosmology of models where the scalar field couples non-minimally to the matter on the brane. This gives rise to a novel scenario where the universe expands from a finite scale factor with an initial period of accelerated expansion, thus avoiding the singularity and flatness problem of the standard big-bang model.

The self-gravitating spherically symmetric thin shells built of orbiting particles are studied. Two new features are found. It is the minimal possible value for the angular momentum of particles, above which elliptic orbits become possible. And the coexistence of both the wormhole solutions and the elliptic or hyperbolic orbits for the same values of parameters (but different initial conditions). Possible applications of this results to astrophysics and quantum black holes are briefly discussed.

A covariant criterion for the emission of Cherenkov radiation in the field of a nonlinear gravitational wave is considered within the framework of exact integrable models of particle dynamics and electromagnetic wave propagation. It is shown that a vacuum interacting with curvature can give rise to Cherenkov radiation. The conically shaped spatial distribution of radiation is derived and its basic properties are discussed.

We found a consistent equation of reheating after inflation which shows that for small quantum fluctuations the frequencies of resonance are slighted different from the standard ones. Quantum interference is taken into account and we found that at large fluctuations the process mimics very well the usual parametric resonance, but proceeds in a different dynamical way. The analysis is made in a toy quantum mechanical model and we discuss further its extension to quantum field theory.