Table of contents

The Editorial Board of Classical and Quantum Gravity recently met to discuss the state of the journal and of the subjects covered. They continue to be impressed by the vigour and vitality of the general area. New topics continue to arise and old ones to mature and deepen. In some areas techniques and understanding have reached a fairly refined level and questions which once seemed out of reach no longer seem beyond our grasp. At the same time there is the ever present need to maintain standards if this progress is to continue and not stall. These general trends in the field have been reflected in our submissions and the reponses of our referees to these submissions. In the light of those comments and as a result of our discussions the Board have decided to draw up a set of guidelines additional to IOP Publishing's standard guidelines to referees. These are reprinted below.

Gary Gibbons Honorary Editor

Instructions to Referees from the Editorial Board

Referees are asked to bear in mind the following points:

(1) The problem considered should have a sound motivation (a statement that the problem has been previously considered by X, Y and Z is not adequate motivation).

(2) A paper should contain a carefully written conclusion, summarising what has been learned and why it is interesting and useful.

In addition, referees are asked to take into account that classical relativity has developed into a mature discipline, which has led to changes in the standards concerning what is significant and worthy of publication, in particular in the area of exact solutions.

(3) The discovery of a new exact solution does not justify publication simply for its own sake. Justification for publishing a new solution would be provided by showing, for example, that it has an interesting physical application or unusual geometrical properties, or that it illustrates an important mathematical point. The onus is on the author to provide convincing evidence that the solution is in fact new.

(4) The development of a new technique or formalism for finding solutions of the field equations does not represent a sufficient advance to justify publication, unless the method is applied successfully (see (3) above).

Ultracompact stars - if they exist - have a unique signature: a discrete spectrum of slowly damped gravitational-wave quasinormal modes. It is known that this feature is due to a potential well present for stars with R<3M. In this letter we show that the appearance of this well is essentially due to the non-Newtonian behaviour of the centrifugal potential: here we explain this behaviour adopting the optical geometry point of view. This insight leads us to an approximation, valid for highly compact stars, by which the real part of the spectrum is easily computed with good accuracy.

Covariant actions for the bosonic fields of D = 10 IIB supergravity are constructed with the help of a single auxiliary scalar field in a formulation with an infinite series of auxiliary (anti-)self-dual 5-form fields.

The Hilbert action is derived for a simplicial geometry. I recover the usual Regge calculus action by way of a decomposition of the simplicial geometry into four-dimensional cells defined by the simplicial (Delaunay) lattice as well as its dual (Voronoi) lattice. Within the simplicial geometry, the Riemann scalar curvature, the proper 4-volume, and hence, the Regge action is shown to be exact, in the sense that the definition of the action does not require one to introduce an averaging procedure or a sequence of continuum metrics which were common in all previous derivations. It appears that the unity of these two dual lattice geometries is a salient feature of Regge calculus.

The Jackiw - Teitelboim gauge formulation of (1 + 1)-dimensional gravity allows us to relate different gauge-fixing conditions to integrable hierarchies of evolution equations. We show that the equations for the zweibein fields can be written as a pair of time-reversed evolution equations of the reaction - diffusion type, admitting dissipative solutions. The spectral parameter for the related Lax pair appears as the constant-valued spin connection associated with the SO(1,1) gauge symmetry. Spontaneous breaking of the non-compact symmetry and irreversible evolution are discussed.

Four- and five-dimensional extremal black holes with nonzero entropy have simple presentations in M-theory as gravitational waves bound to configurations of intersecting M-branes. We discuss realizations of these objects in matrix models of M-theory, investigate the properties of 0-brane probes, and propose a measure of their internal density. A scenario for black-hole dynamics is presented.

We compute the entropy of 5D black holes carrying up to three charges using matrix theory.

We study the interaction of a massless quantized spinor field with the gravitational field of N parallel static cosmic strings by using a perturbative approach. We show that the presence of more than one cosmic string gives rise to an additional contribution to the energy density of vacuum fluctuations, thereby leading to a vacuum force of attraction between two parallel cosmic strings.

For most measures in two-dimensional quantum Regge calculus proposed in the literature we show that the average values of link lengths l, , do not exist for sufficiently high powers of n. In particular, this is also true for the nonlocal DeWitt-like measure introduced by Regge and Lund. Thus the concept of length has no natural definition in this formalism and a generic manifold degenerates into spikes. This might explain the failure of quantum Regge calculus to reproduce the continuum results of two-dimensional quantum gravity. It points to severe problems for the Regge approach in higher dimensions.

The conformal equivalence between the Jordan and the Einstein frames can be used in order to search for exact solutions in general theories of gravity in which scalar fields are coupled with geometry in a standard or in a nonstandard way. In the cosmological arena a relevant role is played by the time parameter in which dynamics is described. In this paper we discuss the problem of conformal equivalence between a given nonstandard coupled model and the corresponding standard one. We analyse in detail the cosmological case and we see that, together with this, and through a careful analysis of the cosmological parameters and , it is possible to contribute to the discussion on which is the physical system.

In this paper, we discuss a possible method of finding cosmological exact solutions in the context of nonstandard coupled gravity theories. We consider whether Noether symmetries, present in the cosmological `point-like' Lagrangian, are preserved under the conformal transformation which reduces a given nonstandard coupled model to the corresponding standard coupled one. We see that Noether symmetries are conformally preserved in a general way.

The 1-loop effective potential for gauge models in static de Sitter space at finite temperatures is computed by means of the -function method. We found a simple relation which links the effective potentials of gauge and scalar fields at all temperatures.

In the de Sitter invariant and zero-temperature states the potential for the scalar electrodynamics is explicitly obtained, and its properties in these two vacua are compared. In this theory the two states are shown to behave similarly in the regimes of very large and very small radii a of the background space. For the gauge symmetry broken in the flat limit there is a critical value of a for which the symmetry is restored in both quantum states.

Moreover, the phase transitions which occur at large or small a are of the first or second order, respectively, regardless of the vacuum considered. The analytical and numerical analysis of the critical parameters of the above theory is performed. We also established a class of models for which the kind of phase transition occurring depends on the choice of the vacuum.

The -function of a massive scalar field near a cosmic string is computed and then employed to find the vacuum fluctuation of the field. The vacuum expectation value of the energy - momentum tensor is also computed using a point-splitting approach and employed to find the back-reaction on the background metric. The results obtained could also be useful for the finite-temperature Rindler space theory.

A fuzzy version of the ordinary round 2-sphere has been constructed with an invariant curvature. We here consider linear connections on arbitrary fuzzy surfaces of genus zero. We shall find as before that they are more or less rigidly dependent on the differential calculus used, but that a large number of the latter can be constructed which are not covariant under the action of the rotation group. For technical reasons we have been forced to limit our considerations to fuzzy surfaces which are small perturbations of the fuzzy sphere.

We find that the momentum conjugate to the relative distance between two gravitating particles in their centre-of-mass frame is a hyperbolic angle. This fact suggests that momentum space can be defined consistently on a hyperboloid. We investigate the effect of quantization on this curved momentum space. The coordinates are represented by non-commuting Hermitian operators. We also find that there is a smallest distance between the two particles of one quarter of the Planck length.

We present a unified way of analysing the quantum generation process of cosmological perturbations in generalized gravity theories. We consider a situation where an accelerated expansion phase of the early universe is realized in a particular generic phase of the generalized gravity. We take the perturbative semiclassical approximation, which treats the perturbed parts of the metric and matter fields as quantum mechanical operators. Our generic results include the conventional power-law and exponential inflations in Einstein gravity, and the pole-like inflations available in a class of generalized gravity theories without potential as special cases. Using a conserved variable in the large scale, independent of the changes in the underlying gravity, we can derive the generated classical spectra of the hydrodynamic variables in the recent Einstein era. We also show that the conformal transformation properly reduces the (quantum) results derived in the original frame of generalized gravity to the ones in Einstein gravity.

Colombeau's theory of generalized functions is used to calculate the contributions, at the rotation axis, to the distributional curvature for a time-dependent radiating cosmic string, and hence the mass per unit length of the string source. This mass per unit length is compared with the mass at null infinity, giving evidence for a global energy conservation law.

We generalize previous work on the energy - momentum tensor distribution of the Kerr geometry by extending the manifold structure into the negative mass region. Since the extension of the flat part of the Kerr - Schild decomposition from one sheet to the double cover develops a singularity at the branch surface, we have to take its non-smoothness into account. It is, however, possible to find a geometry within the generalized Kerr - Schild class that is, in the Colombeau sense, associated to the maximally analytic Kerr metric.

A recently proposed nonlinear transport equation is used to model bulk viscous cosmologies that may be far from equilibrium, as happens during viscous fluid inflation or during reheating. The asymptotic stability of the de Sitter and Friedmann solutions is investigated. The former is stable for bulk viscosity index q<1 and the latter for q>1. New solutions are obtained in the weakly nonlinear regime for q = 1. These solutions are singular and some of them represent a late-time inflationary era.

Using the continuity of the scalar (the mass aspect) at null infinity through , we show that the space of radiative solutions of general relativity can be foliated by identifying each leaf with the value of at . We then show that each non-trivial leaf has a natural intrinsic symplectic form which, given the available geometric structure, does not admit a unique extension to the full solution space.

A Hilbert space structure is then constructed for every point on each leaf. Since there is no natural correspondence between the Hilbert spaces of different leaves, they define superselection sectors on the space of asymptotic quantum states.

Starting from the exact non-linear description of matter and radiation, a fully covariant and gauge-invariant formula for the observed temperature anisotropy of the cosmic microwave background radiation, expressed in terms of the electric and magnetic parts of the Weyl tensor, is obtained by integrating photon geodesics from last scattering to the point of observation today. This improves and extends earlier work by Russ et al where a similar formula was obtained by taking first-order variations of the red-shift. In the case of scalar (density) perturbations, is related to the harmonic components of the gravitational potential and the usual dominant Sachs - Wolfe contribution to the temperature anisotropy is recovered, together with contributions due to the time variation of the potential (Rees - Sciama effect), entropy and velocity perturbations at last scattering and a pressure suppression term important in low density universes. We also explicitly demonstrate the validity of assuming that the perturbations are adiabatic at decoupling and show that if the surface of last scattering is correctly placed and the background universe model is taken to be a flat dust-dominated Friedmann - Robertson - Walker model (FRW), then the large-scale temperature anisotropy can be interpreted as being due to the motion of the matter relative to the surface of constant temperature which defines the surface of last scattering on those scales.

A cylindrically-symmetric perfect-fluid spacetime with no curvature singularity is shown. The equation of state for the perfect fluid is that of a stiff fluid. The metric is diagonal and non-separable in comoving coordinates for the fluid. It is proven that the spacetime is geodesically complete and globally hyperbolic.

We derive a general integral formula on an embedded hypersurface for general relativistic spacetimes. Suppose the hypersurface is foliated by two-dimensional compact `sections' . Then the formula relates the rate of change of the divergence of outgoing light rays integrated over under change of section to geometric (convexity and curvature) properties of and the energy-momentum content of the spacetime. We derive this formula using the Sparling - Nester - Witten identity for spinor fields on the hypersurface by appropriate choice of the spinor fields. We discuss several special cases which have been discussed in the literature before, most notably the Bondi mass loss formula.

Point sources, which are conical singularities in (2 + 1)-dimensional gravity, as well as the BTZ black hole, modify the global curvature of the space giving rise to self-interaction effects on classical fields. In this work we study the electrostatic self-interaction of a point charge either in the presence of a point mass source or a stationary BTZ black hole in (2 + 1)-dimensional gravity with a cosmological constant . Exact expressions are obtained for the self-force in all cases studied.

The observation that the (2 + 1)-dimensional BTZ black hole can be obtained as a quotient space of anti-de Sitter space leads one to ask what causal behaviour other such quotient spaces can display. In this paper we answer this question in 2 + 1 and 3 + 1 dimensions when the identification group has one generator. Among other things we find that there does not exist any 3 + 1 generalization of the rotating BTZ hole. However, the non-rotating generalization exists and exhibits some unexpected properties; for example, it turns out to be non-static and to possess a non-trivial apparent horizon.

Wils has recently investigated pure radiation metrics which are conformal to a vacuum spacetime. It is shown here that, contrary to his claim, he did not find all such solutions. The metrics he found were of type N (or O) and the conformal factor was independent of the radial coordinate. The form of the metric depended on whether the spin coefficient vanished or not. We find that in the case there are additional type O solutions, some of which have only a radially dependent conformal factor and that in the case, in addition to the type N and type O solutions found by Wils, there are type III pure radiation metrics which are conformally Ricci flat. It is proved that this exhausts the class of conformally Ricci flat pure radiation solutions of Einstein's equations. For all type O solutions when , and for some type O solutions in the case, two conformal factors are found, one dependent on the radial coordinate, the other independent of it, indicating that these spaces possess a conformal symmetry.

In a spherically symmetric spacetime we find the general solution for a relativistic star in hydrostatic equilibrium having the spheroidal geometry for the 3-space embedded in 4-Euclidean space. The parameter is the measure of spheroidal character and determines the physical properties of the star. It has a lower bound ; stars with smaller mass to radius ratio can occur for all allowed while ultracompact stars, having ratios between 1/3 and 1/2, will have . It turns out that a wide range of values of can represent objects with the fluid density of a neutron star. The model is shown to possess all the desirable physical features.

We present two completely explicit families of dust cosmological models admitting a maximal two-dimensional group of isometries acting on spacelike surfaces. As far as we know, these are the first (algebraically general) explicit solutions of this kind. Some remarkable properties are: their simplicity, the richness of the singularity structure, and the vanishing of .

We study the spherical gravitational collapse of a compact object under the approximation that the radial pressure is identically zero, and the tangential pressure is related to the density by a linear equation of state . It turns out that the Einstein equations can be reduced to the solution of an integral for the evolution of the area radius. We show that for positive k there is a finite region near the centre which necessarily expands outwards, if collapse begins from rest. This region could be surrounded by an inward moving one which could collapse to a singularity - any such singularity will necessarily be spacelike. If this collapsing shell exists it might, in turn, be surrounded by a second expanding region. For negative k the entire object collapses inwards, but any singularities that could arise are not naked, except possibly at the centre. Thus the nature of the evolution is very different from that of dust, even when k is infinitesimally small. In the case of collapsing dust, there are certain initial configurations in which the collapse leads to the formation of a naked singularity.

The general, energy - momentum tensor for a dynamical, spinning string fluid in general relativity is presented using the Ray - Hilbert variational principle. The calculations are given for both the standard and the extended thermodynamics versions in which the latter includes both the spin and string as thermodynamic variables. Both versions yield the same Fermi - Walker transport of the spin with a correction term due to the string. As an unexpected general feature, it is shown that the string and spin are dual 2-forms. Examples of solutions to the field equations are given for the extension of static black holes for non-spinning, string fluids to stationary, slowly rotating black holes for spinning string fluids. These solutions are then compared with solutions obtained from the postulated energy - momentum tensor of Letelier. The general feature of these solutions for positive density is that the spin causes the event horizon for the stationary black hole to contract whether or not the spin is considered as a thermodynamic variable.

We look for manifestations of the effects of torsion in the low-energy limit in the context of Einstein - Cartan - Dirac theory (or any theory of gravity in which the torsion tensor is purely axial). To proceed, we introduce the mathematical law governing the transport of orthonormal bases or tetrads in a spacetime with torsion. This law is applied to compute the metric and connection in a rotating and accelerating frame, or laboratory. A spin- particle is placed in this rotating and accelerating frame and the low-energy limit of the Dirac equation is taken by means of the Foldy - Wouthuysen transformation. In addition to obtaining the Bonse - Wroblewski phase shift due to acceleration, Sagnac-type effects, rotation - spin couplings of the Mashhoon type, redshift of the kinetic energy and the spin - orbit coupling term of Hehl and Ni, we also obtain several interesting and significant terms as a consequence of introducing torsion into spacetime. We give a detailed interpretation of these additional terms and discuss their observability in the light of current well-known experimental techniques.