Table of contents

Classical and Quantum Gravity (CQG) welcomes articles on experimental gravitation. This includes articles on instrumentation that is mostly of interest for gravitational experiments, as long as the relationship to gravitation is clearly explained in the paper. Experimental authors should also take into account that the readership of CQG is broad, consisting of theorists and experimentalists. It is therefore beneficial to include in the introduction a summary that places the findings in a meaningful context for such a readership.

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Continuing on from previous works, we present a cosmological model in which dark matter and dark energy are modelled by scalar fields Φ and Ψ, respectively, endowed with the scalar potentials V(Φ) = V_o[cosh (λ√κ_oΦ) - 1] and (Ψ) = _o[sinh (α√κ_oΨ)]^β. This model contains a 95% scalar field. We obtain that the scalar dark matter mass is m_Φ~10^-26 eV. The solution obtained allows us to recover the success of standard cold dark matter. The implications on the formation of structure are reviewed. We obtain that the minimal cut-off radio for this model is r_c ~ 1.2 kpc.

We develop a new algorithm for the quantization of systems with first-class constraints. Our approach lies within the (History Projection Operator) continuous-time histories quantization programme. In particular, the Hamiltonian treatment (either classical or quantum) of parameterized systems is characterized by the loss of the notion of time in the space of true degrees of freedom (i.e. the `problem of time'). The novel temporal structure of the HPO theory (two laws of time transformation that distinguish between the temporal logical structure and the dynamics) persists after the imposition of the constraints, hence the problem of time does not arise. We expound the algorithm for both the classical and quantum cases and apply it to simple models.

We use computational algorithms recently developed by ourselves to study completely four index divergence-free quadratic in Riemann tensor polynomials in GR. Some results are new and others reproduce and/or correct known ones. The algorithms are part of a Mathematica package called Tools of Tensor Calculus (TTC).

A two-parameter cylindrically symmetric solution of Einstein's equations is derived for a perfect fluid of finite radius in steady rigid-body rotation. The solution is physically well behaved, with the equation of state, µ + 3p = constant, without singularity and of regular axis. The spacetime is of Petrov type D. The metric is matched at the boundary by a vacuum solution, leaving one free parameter in the complete metric.

This paper develops a theory of thin shells within the context of the Einstein-Cartan theory by extending the known formalism of general relativity. In order to perform such an extension, we require the general non-symmetric stress-energy tensor to be conserved leading, as Cartan pointed out himself, to a strong constraint relating the curvature and the torsion of spacetime. When we restrict ourselves to the class of spacetimes satisfying this constraint, we are able to properly describe thin shells and derive the general expression of the surface stress-energy tensor both in its four-dimensional and in its three-dimensional intrinsic form. We finally derive a general family of static solutions of the Einstein-Cartan theory exhibiting a natural family of null hypersurfaces and use it to apply our formalism to the construction of a null shell of matter.

An interaction between a gravitational wave and the polarization vector of an electromagnetic wave is described in which the polarization vector rotates about the direction of propagation. If a resonant condition can be established with the electromagnetic wave always experiencing the same phase of the gravitational wave then the effect is cumulative and can be enhanced linearly by repeated circuits of a closed loop. When implemented with realistic experimental apparatus, a detector sensitive to gravitational waves at very high frequencies can be envisaged, in a frequency range where the signals are expected to be from cosmological sources at very early moments in the Universe.

Measurement of the equivalence principle violating (EPV) quadrupole and other multipole moments of Earth in a space test of the equivalence principle (STEP) can reveal features of the new force's coupling strength to matter which are not obtainable from measurements of the free fall rate differences among various materials `dropped' in that future experiment. The Earth's EPV force field may include a dipole moment due to asymmetric distribution of the continents, and a quadrupole moment which differs from that of gravity due to the Earth's core-mantle compositional difference. Although the near-isostacy condition of the Earth crust substantially suppresses the crust's contributions to the higher gravity multipole moments of our planet, this will not necessarily be the case for the moments of any EPV force field detected by a STEP mission.

We derive and analyse exact static solutions to the gravitating O(3) σ model with a cosmological constant in (2+1) dimensions. Both signs of the gravitational and cosmological constants are considered. Our solutions include geodesically complete spacetimes, and two classes of black holes.

The aim of this paper is to examine some obtained exact solutions of the Einstein-Maxwell equations, in particular their properties from a chronological point of view. Each of our spacetimes is stationary and cylindrically symmetric and is filled with a perfect fluid that is electrically charged. There are two classes of solutions and examples of each are investigated. We give examples of the first class for both the vanishing and non-vanishing Lorentz force.

Self-similar, spherically symmetric cosmological models with a perfect fluid and a scalar field with an exponential potential are investigated. New variables are defined which lead to a compact state space, and dynamical systems methods are utilized to analyse the models. Due to the existence of monotonic functions, global dynamical results can be deduced. In particular, all of the future and past attractors for these models are obtained and the global results are discussed. The essential physical results are that initially expanding models always evolve away from a massless scalar field model with an initial singularity and, depending on the parameters of the models, either recollapse to a second singularity or expand forever towards a flat power-law inflationary model. The special cases in which there is no barotropic fluid and in which the scalar field is massless are considered in more detail in order to illustrate the asymptotic results. Some phase portraits are presented and the intermediate dynamics and hence the physical properties of the models are discussed.

The general metric for N-dimensional spherically symmetric and conformally flat spacetimes is given, and all the homogeneous and isotropic solutions for a perfect fluid with the equation of state p = αρ are found. These solutions are then used to model the gravitational collapse of a compact ball. It is found that when the collapse has continuous self-similarity, the formation of black holes always starts with zero mass, and when the collapse has no such symmetry, the formation of black holes always starts with a mass gap.

We investigate whether the isotropy problem is naturally solved in inflationary cosmologies inspired by string theory, so called pre-big-bang cosmologies. We find that, in contrast to what happens in the more common `potential inflation' models, initial anisotropies do not decay during pre-big-bang inflation.

In a recent paper, Carot et al considered carefully the definition of cylindrical symmetry as a specialization of the case of axial symmetry. One of their propositions states that if there is a second Killing vector, which together with the one generating the axial symmetry, forms the basis of a two-dimensional Lie algebra, then the two Killing vectors must commute, thus generating an Abelian group. In this comment a similar result, valid under considerably weaker assumptions, is recalled: any two-dimensional Lie transformation group which contains a one-dimensional subgroup whose orbits are circles, must be Abelian. The method used to prove this result is extended to apply to three-dimensional Lie transformation groups. It is shown that the existence of a one-dimensional subgroup with closed orbits restricts the Bianchi type of the associated Lie algebra to be I (Abelian), II, III, VII_{q = 0}, VIII or IX. The relationship between the present approach and that of the original paper is discussed.