Table of contents

The Editorial Board of Classical and Quantum Gravity met recently to discuss the state of the journal and the subjects covered. They noted the vigour and vitality of the journal and how it is attracting a growing number of high quality submissions in theoretical and experimental gravity as well as numerical relativity. However, the Board thought that the number of articles in relativistic astrophysics and cosmology is not as as large as they would wish.

This is something that the Board would very much like to change. As a step in that direction they would like to draw attention to their strong desire to see more high quality articles in this area published in the journal. Accordingly, they would like to extend a warm welcome to those colleagues working on theoretical aspects of neutron stars, astrophysical black holes, cosmology at large redshifts, studies of large scale structure, very early Universe cosmology, also gravitational lenses and waves, and urge them to submit their work to Classical and Quantum Gravity.

A discrete symmetry of the four-dimensional string effective action is employed to derive spatially homogeneous and inhomogeneous string cosmologies from vacuum solutions of general relativity that admit two commuting spacelike Killing vectors. In particular, a tilted Bianchi type V cosmology is generated from a vacuum type VI solution and a plane wave solution with a bounded and oscillating dilaton field is found from a type VII model. Further applications are briefly discussed.

A review of recent progress in string theory concerning the Bekenstein formula for black hole entropy is given. Topics discussed include p-branes, D-branes and supersymmetry; the correspondence principle; the D- and M-brane approach to black hole entropy; the D-brane analogue of Hawking radiation and information loss; D-branes as probes of black holes and the matrix theory approach to charged and neutral black holes. Some introductory material is included, as are some very brief remarks on the AdS/CFT correspondence.

In this paper we analyse the noise level induced by changes in the mass density distribution around the Virgo interferometric antenna. These stochastic mass density fluctuations generate a gravitational field which couples directly to the mirrors of the optical apparatus, and it could be relevant if the planned final sensitivity of the Virgo interferometer is to be reached.

A worth function is constructed for any fitted parameter of the lunar laser ranging (LLR) model. It quantifies the reduction in the formal noise uncertainty of the parameter's estimated value which will result from an additional LLR observation made at a particular future time. This function is applied to optimizing the measurement of three effects in gravitational theory which are scrutinized by LLR - possible violation of the universality of gravitational free-fall rates (the so-called violation of the equivalence principle), geodetic precession of the local inertial frame and possible time variation of Newton's coupling parameter, G. An asymmetry in the present data distribution (more observations exist between quarter and full moon phase than between quarter and new moon phase) is found to strongly shape the worth function for the equivalence principle test, so that future observations on the new moon side of quarter moon are of much higher value. The worth function for the moon's synodic rate, a parameter central to determining both the geodetic precession of local inertial space and any time variation of Newton's G, is found to be quite variable through the synodic month and with those variations also differing significantly from one month to another. The lunar nodical rate is also important for determining the geodetic precession, helping to eliminate uncertainty due to a weakly known lunar quadrupole moment parameter. Its worth function is found to not only vary through the month and year, but also to vary noticeably by the hour during a typical observation session. Shaping the future LLR observation schedule to take advantage of these worth function variations can appreciably increase the rate of improvement in the measurement precisions for the scientific parameters from LLR. Applying the worth function a priori to optimize observation times in other future ranging experiments can significantly increase the sensitivity of the resulting data to model parameters of scientific interest, and properties of such optimal distributions are explored in an appendix.

The thermodynamic free energy F is calculated for a gas whose particles are the quantum excitations of a piecewise uniform bosonic string. The string consists of two parts of length and , endowed with different tensions and mass densities, adjusted in such a way that the velocity of sound always equals the velocity of light. The explicit calculation is done under the restrictive condition that the tension ratio approaches zero. Also, the length ratio is assumed to be an integer. The expression for F is given in an integral form, in which s is present as a parameter. For large values of s, the Hagedorn temperature becomes proportional to the square root of s.

A geometrical construction of superconformal transformations in six-dimensional (2, 0) superspace is proposed. Superconformal Killing vectors are determined. It is shown that the transformation of the tensor multiplet involves a zero curvature non-trivial cochain.

We consider the GUT-like model with two scalar fields which has infinitesimal deviation from the conformal invariant fixed point in the high-energy region. In this case the dominant quantum effect is the conformal trace anomaly and the interaction between the anomaly-generated propagating conformal factor of the metric and the usual dimensional scalar field. This interaction leads to the renormalization group flow from the conformal point. In the supersymmetric conformal invariant model such an effect produces a very weak violation of sypersymmetry at lower energies.

The possibility of embedding arbitrary causal sets into manifolds is investigated. This issue is relevant to the nature of any quantum theory of gravity based upon causal sets. It is also important when causal sets are merely used as an alternative method of discretizing calculations within the realm of classical general relativity.

The Euclidean quantum amplitude to go between data specified on an initial and a final hypersurface may be approximated by the tree amplitude

where is the Euclidean action of the classical solution joining the initial and final data. In certain cases the tree amplitude is exact. We study , and hence the quantum amplitude, in the case of a spherically symmetric Riemannian gravitational field coupled to a spherically symmetric scalar field. The classical scalar field obeys an elliptic equation, which we solve using relaxation techniques, in conjunction with the field equations giving the gravitational field. An example of the transition from linearity to nonlinearity is presented and power-law behaviour of the action is demonstrated.

We compute the running of the cosmological constant and Newton's constant at sub-Planckian energies, taking into account the effect of quantum fields with any spin between 0 and 2. We find that Newton's constant does not vary appreciably but the cosmological constant can change by many orders of magnitude when one goes from cosmological scales to typical elementary particle scales. In the extreme infrared, zero modes drive a positive cosmological constant to zero.

We calculate partition functions for lens spaces up to p = 8 and for genus-1 and -2 handlebodies , in the Turaev - Viro framework. These can be interpreted as transition amplitudes in three-dimensional quantum gravity. In the case of lens spaces these are vacuum-to-vacuum amplitudes , whereas for the 1- and 2-handlebodies , they represent genuinely topological transition amplitudes and , respectively.

We show that the equations of motion of two-dimensional dilaton gravity conformally coupled to a scalar field can be reduced to a single nonlinear second-order partial differential equation when the coordinates are chosen to coincide with the two scalar fields, the matter field f and the dilaton , which are present in the theory. This result may help solve and understand two- and higher-dimensional classical and quantum gravity.

The singularity structure of cosmological models whose matter content consists of a scalar field with arbitrary non-negative potential is discussed. The special case of spatially flat FRW spacetime is analysed in detail using a dynamical systems approach which may readily be generalized to more complicated spacetimes. It is shown that for a very large and natural class of models a simple and regular past asymptotic structure exists. More specifically, there exists a family of solutions which is in continuous one-to-one correspondence with the exactly integrable massless scalar field cosmologies, this correspondence being realized by a unique asymptotic approximation. The set of solutions which do not fall into this class has measure zero. The significance of this result to the cosmological initial-value problem is discussed briefly.

We investigate geodesics in non-homogeneous vacuum pp-wave solutions and demonstrate their chaotic behaviour by rigorous analytic and numerical methods. For the particular class of solutions considered, distinct `outcomes' (channels to infinity) are identified, and it is shown that the boundary between different outcomes has a fractal structure. This seems to be the first example of chaos in exact radiative spacetimes.

We develop further our extension of the Ellis - Bruni covariant and gauge-invariant formalism to the general relativistic treatment of density perturbations in the presence of cosmological magnetic fields. We present a detailed analysis of the kinematical and dynamical behaviour of perturbed magnetized FRW cosmologies containing fluid with non-zero pressure. We study the magnetohydrodynamical effects on the growth of density irregularities during the radiation era. Solutions are found for the evolution of density inhomogeneities on small and large scales in the presence of pressure, and some new physical effects are identified.

Exact dynamical equations for a generic dust matter source field in a cosmological context are formulated with respect to a non-comoving Newtonian-like timelike reference congruence and investigated for internal consistency. On the basis of a lapse function N (the relativistic acceleration scalar potential) which evolves along the reference congruence according to , we find that consistency of the quasi-Newtonian dynamical equations is not attained at the first derivative level. We then proceed to show that a self-consistent set can be obtained by linearizing the dynamical equations about a (non-comoving) FLRW background. In this case, on properly accounting for the first-order momentum density relating to the non-relativistic peculiar motion of the matter, additional source terms arise in the evolution and constraint equations describing small-amplitude energy density fluctuations that do not appear in similar gravitational instability scenarios in the standard literature.

Anti-de Sitter space with identified points give rise to black-hole structures. This was first pointed out in three dimensions and generalized to higher dimensions by Aminneborg et al. In this paper, we analyse several aspects of the five-dimensional anti-de Sitter black hole, including its relation to thermal anti-de Sitter space, its embedding in a Chern - Simons supergravity theory, its global charges and holonomies and the existence of Killing spinors.

In this paper, a procedure which gives Euclidean solutions of three-dimensional Einstein - Yang - Mills equations when one has solutions of the Einstein equations is proposed. The method is based on reformulating Yang - Mills theory in such a way that it becomes a gravity. It is applied to find black hole solutions of the coupled Einstein - Yang - Mills equations

With the recent discovery that many aspects of black hole thermodynamics can be effectively reduced to problems in three spacetime dimensions, it has become increasingly important to understand the `statistical mechanics' of the (2 + 1)-dimensional black hole of Bañados, Teitelboim, and Zanelli (BTZ). Several conformal field theoretic derivations of the BTZ entropy exist, but none is completely satisfactory, and many questions remain open: there is no consensus as to what fields provide the relevant degrees of freedom or where these excitations live. In this paper, I review some of the unresolved problems and suggest avenues for their solution.

We derive exact solutions of two-dimensional dilaton gravity coupled to massless spinors for some particular choices of the dilatonic potential. For constant dilatonic potential the model turns out to be completely solvable and the general solution is found. For linear and exponential dilatonic potentials we present the class of exact solutions with a Killing vector.

A generalization of the theory of stellar equilibrium is proposed which involves the possibility of local anisotropy (unequal principal stresses) even if the star is formed by an otherwise perfect fluid. Using this theory, supermassive stars are studied in the post-Newtonian approximation and it is shown that there are equilibrium configurations with local anisotropy having mass above, or entropy below, the standard limit with local isotropy.

The interaction of high-frequency asymptotic waves in general relativistic magnetohydrodynamics will be investigated. It shall be proved that an order-one magnetosonic wave generates a gravitational wave of order three (theorem 1), and an order-two gravitational wave generates a magnetosonic wave of the same order (theorem 2). If the fluid satisfies the limit state equation , then a magnetosonic and a gravitational wave of same phase and of the same order can coexist and interact, each one acting as a source for the other (theorem 3).

A new family within the spherically symmetric two-component dust metrics (Haager G 1997 Class. Quantum Grav. 14 2219) with an additional homothetic vector is investigated in detail. These metrics are regular except for a big bang singularity and can be given by an asymptotic expansion of the metric coefficients for large times after the big bang. Using this family, voids can be described whose edge is not comoving in comparison with its surroundings. A concrete example is given where the edge of the void is contracting, while the dust background is expanding.

We show that there exist maximal globally hyperbolic solutions of the Einstein-dust equations which admit a constant mean curvature Cauchy surface, but are not covered by a constant mean curvature foliation.

A brief summary of results on kinematic self-similarities in general relativity is given. Attention is focused on locally rotationally symmetric models admitting kinematic self-similar vectors. Coordinate expressions for the metric and the kinematic self-similar vector are provided. Einstein's field equations for perfect fluid models are investigated and all the homothetic perfect fluid solutions admitting a maximal four-parameter group of isometries are given.

We make a detailed study of boson star configurations in Jordan - Brans - Dicke theory, studying both equilibrium properties and stability, and considering boson stars existing at different cosmic epochs. We show that these boson stars can be stable at any time of cosmic history, and that equilibrium stars are denser in the past. We analyse three different proposed mass functions for boson star systems. We study how the configurations depend on the value of the Jordan - Brans - Dicke coupling constant, and the properties of the stars under extreme values of the gravitational asymptotic constant. This last point allows us to extract conclusions about the stability behaviour concerning the scalar field. Finally, other dynamical variables of interest, such as the radius, are also calculated. In this regard, it is shown that the radius corresponding to the maximal boson star mass remains roughly the same during cosmological evolution.

We show that almost all metric-affine theories of gravity yield Einstein field equations with a non-null cosmological constant . Under certain circumstances and for any dimension, it is also possible to incorporate a Weyl vector field and therefore the presence of an anisotropy. The viability of these field equations is discussed in view of recent astrophysical observations.

A recent paper by Uzan discusses a covariant formulation to describe a set of interacting gases in terms of macroscopic quantities and certain collision integrals. This letter shows how to formulate the general theory to allow easy integration or approximation of the integrals.

In a recent comment Stewart explains how the results of my article (1998 Class. Quantum Grav. 15 1063) can be recovered from a formalism he developed 27 years ago. I will recall the assumptions of the two approaches and stress their differences.