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.

The Editorial Board

A finite universe naturally supports chaotic classical motion. An ordered fractal emerges from the chaotic dynamics which we characterize in full for a compact two-dimensional octagon. In the classical-to-quantum transition, the underlying fractal can persist in the form of scars, ridges of enhanced amplitude in the semiclassical wavefunction. Although the scarring is weak on the octagon, we suggest possible subtle implications of fractals and scars in a finite universe.

Mechanics of non-rotating black holes was recently generalized by replacing the static event horizons used in standard treatments with `isolated horizons'. This framework is extended to incorporate dilaton couplings. Since there can be gravitational and matter radiation outside isolated horizons, now the fundamental parameters of the horizon, used in mechanics, must be defined using only the localstructure of the horizon, without reference to infinity. This task is accomplished and the zeroth and first laws are established. To complement the previous work, the entire discussion is formulated tensorially, without any reference to spinors.

Solutions of the wave equation in a spacetime containing a thin cosmic string are examined in the context of nonlinear generalized functions. Existence and uniqueness of solutions to the wave equation in the Colombeau algebra is established for a conical spacetime and this solution is shown to be associated with a distributional solution. A concept of generalized hyperbolicity, based on test fields, can be defined for such singular spacetimes and it is shown that a conical spacetime is -hyperbolic.

We consider the force acting on a spinning charged test particle (probe particle) with mass mand charge qin a slowly rotating Kerr-Newman-de Sitter (KNdS) black hole with mass Mand charge Q . We consider the case in which the spin vector of the probe particle is parallel to the angular momentum vector of the KNdS spacetime. We take account of the gravitational spin-spin interaction under the slow rotation limit of the KNdS spacetime. When Q= Mand q= m , we show that the force balance holds including the spin-spin interaction and the motion is approximately the same as that of a particle in de Sitter spacetime. This force cancellation suggests the possibility of the existence of an exact solution of a spinning multi-KNdS black hole.

A study is made of the possible holonomy group types of a spacetime for which the energy-momentum tensor corresponds to a null or non-null electromagnetic field, a perfect fluid or a massive scalar field. The case of an Einstein space is also included. The techniques developed are, in addition, applied to vacuum and conformally flat spacetimes and contrasted with already known results in these two cases. Examples are given.

Irreducible currents with arbitrary spin are constructed in a general spacetime dimension, in the free-field limit and, at the bare level, in the presence of interactions. For the n -dimensional generalization of the (conformal) vector field, the (n /2-1)-form is used. Two-point functions and higher-spin central charges are evaluated at one-loop. As an application, the higher-spin hierarchies generated by the stress tensor operator-product expansion are computed in supersymmetric theories. The results exhibit an interesting universality.

The Penrose method for constructing spherical impulsive gravitational waves is investigated in detail, including alternative spatial sections and an arbitrary cosmological constant. The resulting waves include those that are generated by a snapping cosmic string. The method is used to construct an explicit exact solution of Einstein's equations describing the collision of two non-aligned cosmic strings in a Minkowski background which snap at their point of collision.

We present a fully covariant quantization of the minimally coupled massless field on de Sitter space, thanks to a new representation of the canonical commutation relations. We thus obtain a formalism free of any infrared divergence. Our method is based on a rigorous group-theoretical approach combined with a suitable adaptation (Krein spaces) of the Wightman-Gärding axiomatic for massless fields (Gupta-Bleuler scheme). We make explicit the correspondence between unitary irreducible representations of the de Sitter group and the field theory on de Sitter spacetime. The minimally coupled massless field is associated with a representation which is the lowest term of the discrete series of unitary representations of the de Sitter group. In spite of the presence of negative-norm modes in the theory, no negative energy can be measured: expressions such as n_k1n_k2... |T₀₀ |n_k1n_k2... are always positive.

We report some new exact instantons in general relativity, describing their relevance to cosmology. These solutions are Kähler and fall into the symmetry classes of Bianchi types VI₀and VII₀ , with the matter content of a stiff fluid. The qualitative behaviour of the solutions is presented, and we compare it to the known results of the corresponding self-dual Bianchi solutions. We also give axisymmetric Bianchi VII₀solutions with an electromagnetic field.

The condition for a perfect fluid in the metric-affine extension of the Riemannian spacetime of general relativity is determined. The condition for a pureperfect fluid without any additional interactions imposes a very strong restriction on the continuity relation for the fluid. The effect of this restriction is to remove both the torsion and the Weyl vectors from the field equations. This shows that for matter described entirely by a perfect fluid, the continuity relation for the fluid must take its general relativistic form. This results opens up an entirely new arena in gravitational physics for the systematic investigation of various fluids with additional matter fields in metric-affine geometry. It is also shown for the case of symmetry breaking terms that break projective invariance of the Riemann scalar Lagrangian that the restrictive condition on the perfect fluid can be relaxed; however this method of extending fluids to the full metric-affine geometry, as is already known, will introduce unknown coupling constants into the theory.

An exact, axially symmetric solution for gravity minimally coupled to a scalar field is employed to calculate several effects that might be interesting for astrophysical detection of scalar fields. It is found that, as the ratio Q_s /mof the scalar charge to the mass parameter of the metric increases, the difference with general relativity predictions becomes larger, which can be used to set an upper limit for this ratio, both from the weak- and the strong-field regimes. For the latter, we reanalysed the strong light deflection near a compact star, previously studied in the context of general relativity, for which we found a discrepancy between a few and 80%, depending on the value of Q_s /m ; although this effect is very difficult to observe even for general relativity, it would put a bound on Q_sfrom a strong-field situation. Brief mention is made of what these effects look like in other scalar-tensor theories of gravity.

The Hamiltonian of the gravitational field defined in a bounded region is quantized. The classical Hamiltonian, and starting point for the regularization, is a boundary term required by functional differentiability of the Hamiltonian constraint. It is the quasilocal energy of the system and becomes the ADM mass in asymptopia. The quantization is carried out within the framework of canonical quantization using spin networks. The result is a gauge-invariant, well-defined operator on the Hilbert space induced by the state space on the whole spatial manifold. The spectrum is computed. An alternative form of the operator, with the correct naive classical limit, but requiring a restriction on the Hilbert space, is also defined. Comparison with earlier work and several consequences are briefly explored.

The framework of quantum symmetry reduction is applied to loop quantum gravity with respect to transitively acting symmetry groups. This allows us to test loop quantum gravity in a large class of minisuperspaces and to investigate its features - e.g. the discrete volume spectrum - in certain cosmological regimes. Contrary to previous studies of quantum cosmology (minisuperspace quantizations) the symmetry reduction is carried out not at the classical level but on an auxiliary Hilbert space of the quantum theory before solving the constraints. Therefore, kinematical properties like volume quantization survive the symmetry reduction. In this first part of a series of papers the kinematical framework, i.e. implementation of the quantum symmetry reduction and quantization of Gauß and diffeomorphism constraints, is presented for Bianchi class A models as well as locally rotationally symmetric and spatially isotropic closed and flat models.

Volume operators measuring the total volume of space in a loop quantum theory of cosmological models are constructed. In the case of models with rotational symmetry an investigation of the Higgs constraint imposed on the reduced connection variables is necessary, a complete solution of which is given for isotropic models; in this case the volume spectrum can be calculated explicitly. It is observed that the stronger the symmetry conditions are the smaller is the volume spectrum, which can be interpreted as level splitting due to broken symmetries. Some implications for quantum cosmology are presented.

We analyse the Hamilton-Jacobi action of gravity and matter in the limit where gravity is treated at the background field approximation. The motivation is to clarify when the Wheeler-DeWitt equation leads to the Schrödinger equation in a background geometry. In particular, we investigate the problem of the choice of the background and that of the corrections to the Schrödinger equation associated with this choice. To this end, we first work classically. We determine when the total action, a solution of the constraint equations of general relativity, leads to the matter action in a given background. This is achieved by comparing neighbouring solutions differing in their matter-energy content. To first order in the change of the 3-geometries, the total action splits into an irrelevant background contribution and the usual matter action evaluated in the background. Higher-order terms are governed by the choice of the background geometry and by its `susceptibility'. These properties apply to quantum cosmology when it is described by WKB wavefunctions. We then show that the corrections to these WKB waves and to the background field approximation appear together and remain small when the susceptibility of the background is low.

We present calculations of gyroscope precession in spacetimes described by Levi-Civita and Lewis metrics, under different circumstances. By doing so we are able to establish a link between the parameters of the metrics and observable quantities, thereby providing a physical interpretation for those parameters, without specifying the source of the field.

Relations between the Bondi-Sachs approach and the Penrose conformal technique for asymptotically flat metrics are reviewed. Conditions on the conformal factor and the Ricci tensor are examined in order to compare the two approaches. The Bondi-Sachs coordinates are constructed (up to O(³ )) for a class of Robinson-Trautman metrics. Some solutions within this class (with pure radiation fields) are given.

It is remarked that the computer-generated results (and more) regarding symmetries of the Kerr spacetime recently reported by Jerie et al(1999 Class. Quantum Grav.162885) are well known and that similar results for other standard spacetimes can be obtained by geometrical techniques.

The first superstring revolution, in 1984, was responsible for eliminating 11-dimensional supergravity from the list of candidates for the ultimate theory of nature. The return of 11-dimensional supergravity, in 1995, in a new guise called M-theory in the second superstring revolution is more dramatic than its exit 11 years ago. This is because the duality relationship between all the known string theories is incomplete without M-theory. Though this new avatar of 11-dimensional supergravity entered as a missing piece in the jigsaw puzzle of string dualities, it quickly established its special status by demonstrating that most of the string theories including the chiral ones can be derived from it in some specific limit. Whatever understanding we have of M-theory, so far, is challenging enough to make it one of most exciting subjects for `string theorists', with new results appearing on the net almost everyday. Publication of `The World in Eleven Dimensions', a reprint volume on 11-dimensional supergravity, supermembranes and M-theory is, therefore, very relevant and timely.

This book contains six chapters and 33 papers which nicely cover of the evolution 11-dimensional supergravity from its pre-Kaluza-Klein supergravity days to its new incarnation as M-theory. The first chapter contains the original paper on 11-dimensional supergravity (Cremmer E, Julia B and Scherk J 1978 Phys. Lett.B 76409) as well as papers on Kaluza-Klein compactification of it down to four dimensions.

Though 11-dimensional supergravity was out of fashion in the late 1980s a small set of researchers kept the subject alive. One of the important developments during that time was the discovery of the supermembrane and its realization as a classical solution to the supergravity equations of motion. Chapter 2 contains some of the important papers on this subject, e.g., a paper by de Wit et al, which is relevant to the matrix theory developments in chapter 6.

Chapter 3, contains an excellent collection of papers on the M-5-brane. Most of these papers are relatively new. This is simply because the utility of M-5-branes was understood only recently. Their dynamics, however, is still largely unknown. This chapter contains papers which use M-5-branes to determine the dynamics of compactified M-theory as well as anomalous couplings due to their chiral worldvolume theory.

Papers in the fourth chapter use kappa symmetry to derive the type IIA superstring by double dimensional reduction of the supermembrane in 11 dimensions and study duality in the membrane theory. Other papers in this chapter set the stage for the return of 11-dimensional supergravity. Configurations of M-branes have proved useful in understanding the dynamics of black holes as well as super-Yang-Mills theories in four dimensions. Chapter 5 contains papers on configurations of intersecting M-branes and their applications in black hole physics.

All the papers in chapter 6 are classic papers in M-theory in the second superstring revolution. Each one of them has led to quantum jumps in conceptual understanding of physics of M-theory. It contains papers by Horava and Witten, Banks et aland Maldacena to name a few.

It is obviously impossible to do justice to all the contributors to this subject in a 500 page reprint volume with a huge amount of literature existing on it in the journals. This is where the experience of the editor (Professor M J Duff) has helped in judiciously choosing landmark papers in this field. It is a pleasure to review this reprint volume which contains almost all the major milestones in the 22-year history of this subject. It can serve as a very useful one-spot reference for advanced readers as well as an excellent fast-track introduction to the subject for new entrants, although background knowledge of supersymmetric field theories and, to some extent, of superstrings is needed. The editor's comments at the beginning of the chapters are quite instructive and, as intended, do indeed give a wider perspective. A list of references at the end of every commentary is extensive though not quite exhaustive. It, however, illustrates quite well the level of difficulty involved in choosing 33 papers out of them.