Table of contents

We explore the relationship between classical quasi-normal mode frequencies and black-hole quantum mechanics in 2 + 1 dimensions. Following a suggestion of Hod, we identify the real part of the quasi-normal frequencies with the fundamental quanta of black-hole mass and angular momentum. We find that this identification leads to the correct quantum behaviour of the asymptotic symmetry algebra, and thus of the dual conformal field theory. Finally, we suggest a further connection between quasi-normal mode frequencies and the spectrum of a set of nearly degenerate ground states whose multiplicity may be responsible for the Bekenstein–Hawking entropy.

We use rigorous techniques from numerical analysis of hyperbolic equations in bounded domains to construct stable finite-difference schemes for numerical relativity, in particular for their use in black-hole excision. As an application, we present 3D simulations of a scalar field propagating in a Schwarzschild black-hole background.

We show that the holonomy of the supercovariant connection of IIB supergravity is contained in SL(32, ). We also find that the holonomy reduces to a subgroup of SL(32 − N) ⋉ (⊕^{N 32−N}) for IIB supergravity backgrounds with N Killing spinors. We give the necessary and sufficient conditions for a IIB background to admit N Killing spinors. A IIB supersymmetric probe configuration can involve up to 31 linearly independent planar branes and preserves one supersymmetry.

There is accumulating evidence that (fundamental) scalar fields may exist in nature. The gravitational collapse of such a boson cloud would lead to a boson star (BS) as a new type of a compact object. As with white dwarfs and neutron stars, a limiting mass exists similarly, below which a BS is stable against complete gravitational collapse to a black hole.

According to the form of the self-interaction of the basic constituents and spacetime symmetry, we can distinguish mini-, axidilaton, soliton, charged, oscillating and rotating BSs. Their compactness prevents a Newtonian approximation; however, modifications of general relativity, as in the case of Jordan–Brans–Dicke theory as a low-energy limit of strings, would provide them with gravitational memory.

In general, a BS is a compact, completely regular configuration with structured layers due to the anisotropy of scalar matter, an exponentially decreasing 'halo', a critical mass inversely proportional to the constituent mass, an effective radius and a large particle number. Due to the Heisenberg principle, a completely stable branch exists, and as a coherent state, it allows for rotating solutions with quantized angular momentum.

In this review, we concentrate on the fascinating possibilities of detecting the various subtypes of (excited) BSs: possible signals include gravitational redshift and (micro-)lensing, emission of gravitational waves, or, in the case of a giant BS, its dark matter contribution to the rotation curves of galactic halos.

We describe an accelerating universe model in the context of a scalar–tensor theory. This model is intrinsically closed, and is filled with quintessence-like scalar field components, in addition to the cold dark matter component. With a background geometry specified by the Friedmann–Robertson–Walker metric, we establish conditions under which this closed cosmological model, described in a scalar–tensor theory, may look flat in a genuine Jordan–Brans–Dicke theory. Both models become indistinguishable at low enough redshift.

We investigate the possibility of having an event horizon within several classes of metrics that asymptote to the maximally supersymmetric IIB plane wave. We show that the presence of a null Killing vector (not necessarily covariantly constant) implies an effective separation of the Einstein equations into a standard and a wave component. This feature may be used to generate new supergravity solutions asymptotic to the maximally supersymmetric IIB plane wave, starting from standard seed solutions such as branes or intersecting branes in flat space. We find that in many cases it is possible to preserve the extremal horizon of the seed solution. On the other hand, non-extremal deformations of the plane wave solution result in naked singularities. More generally, we prove a no-go theorem against the existence of horizons for backgrounds with a null Killing vector and which contain at most null matter fields. Further attempts at turning on a non-zero Hawking temperature by introducing additional matter have proved unsuccessful. This suggests that one must remove the null Killing vector in order to obtain a horizon. We provide a perturbative argument indicating that this is in fact possible.

Present models describing the interaction of quantum Maxwell and gravitational fields predict a breakdown of Lorentz invariance and a non-standard dispersion relation in the semiclassical approximation. Comparison with observational data, however, does not support their predictions. In this work we introduce a different set of ab initio assumptions in the canonical approach, namely that the homogeneous Maxwell equations are valid in the semiclassical approximation, and find that the resulting field equations are Lorentz invariant in the semiclassical limit. We also include a phenomenological analysis of possible effects on the propagation of light, and their dependence on energy, in a cosmological context.

We consider asymptotically anti-de Sitter black holes in d-spacetime dimensions in the thermodynamically stable regime. We show that the Bekenstein–Hawking entropy and its leading order corrections due to thermal fluctuations are reproduced by a weakly interacting fluid of bosons and fermions ('dual gas') in Δ = α(d − 2) + 1 spacetime dimensions, where the energy–momentum dispersion relation for the constituents of the fluid is assumed to be = κp^α. We examine implications of this result for entropy bounds and the holographic hypothesis.

A hyper-Kähler 4-metric with a triholomorphic SU(2) action gives rise to a family of confocal quadrics in Euclidean 3-space when cast in the canonical form of a hyper-Kähler 4-metric with a triholomorphic circle action. Moreover, at least in the case of geodesics orthogonal to the U(1) fibres, both the covariant Schrödinger and the Hamilton–Jacobi equations are separable and the system integrable.

In this paper, some gravitomagnetic effects are explored in the presence of cosmic strings. In particular, the gravitomagnetic clock effects and gyroscope precession are considered in the equatorial plane of a spacetime that is the nonlinear superposition of a Kerr black hole with a cosmic string along its axis of rotation. Moreover, an exact solution of the Einstein field equations corresponding to the Gödel universe with a cosmic string is introduced. The influence of the cosmic string on the gravitomagnetic effects in this spacetime is briefly studied.

It is shown that linearized gravitational radiation confined in a cavity can achieve thermal equilibrium if the mean density of the radiation and the size of the cavity satisfy certain constraints.

A number of background-independent quantization procedures have recently been employed in 4D nonperturbative quantum gravity. We investigate and illustrate these techniques and their relation in the context of a simple 2D topological theory. We discuss canonical quantization, loop or spin network states, path integral quantization over a discretization of the manifold, spin foam formulation and the fully background-independent definition of the theory using an auxiliary field theory on a group manifold. While several of these techniques have already been applied to this theory by Witten, the last one is novel: it allows us to give a precise meaning to the sum over topologies, and to compute background-independent and, in fact, 'manifold-independent' transition amplitudes. These transition amplitudes play the role of Wightman functions of the theory. They are physical observable quantities, and the canonical structure of the theory can be reconstructed from them via a C* algebraic GNS construction. We expect an analogous structure to be relevant in 4D quantum gravity.

Considering complex n-dimension Calabi–Yau homogeneous hypersurfaces _n with discrete torsion and using the Berenstein and Leigh algebraic geometry method, we study fractional D-branes that result from stringy resolution of singularities. We first develop the method introduced by Berenstein and Leigh (Preprint hep-th/0105229) and then build the non-commutative (NC) geometries for orbifolds = _n/Z_n+2ⁿ with a discrete torsion matrix t_ab = exp[i2π/n+2(η_ab − η_ba)], η_ab ∊ SL(n, Z). We show that the NC manifolds ^(nc) are given by the algebra of functions on the real (2n + 4) fuzzy torus _βij²⁽ⁿ⁺²⁾ with deformation parameters β_ij = exp i2π/n+2[(η_ab⁻¹ − η_ba⁻¹)q^a_iq^b_j] with q^a_i being charges of Zⁿ_n+2. We also give graphic rules to represent ^(nc) by quiver diagrams which become completely reducible at orbifold singularities. It is also shown that regular points in these NC geometries are represented by polygons with (n + 2) vertices linked by (n + 2) edges while singular ones are given by (n + 2) non-connected loops. We study the various singular spaces of quintic orbifolds and analyse the varieties of fractional D-branes at singularities as well as the spectrum of massless fields. Explicit solutions for the NC quintic ^(nc) are derived with details and general results for complex n-dimension orbifolds with discrete torsion are presented.

The black-hole entropy calculation for type I isolated horizons, based on loop quantum gravity, is extended to include non-minimally coupled scalar fields. Although the non-minimal coupling significantly modifies quantum geometry, the highly non-trivial consistency checks for the emergence of a coherent description of the quantum horizon continue to be met. The resulting expression of black-hole entropy now depends also on the scalar field precisely in the fashion predicted by the first law in the classical theory (with the same value of the Barbero–Immirzi parameter as in the case of minimal coupling).

A linear evolution of the cosmological scale factor is a feature in several models designed to solve the cosmological constant problem via a coupling between scalar or tensor classical fields to the spacetime curvature as well as in some alternative gravity theories. In this paper, by assuming a general time dependence of the scale factor, R ∼ t^α, we investigate observational constraints on the dimensionless parameter α from measurements of the angular size for a large sample of milliarcsecond compact radio sources. In particular, we find that a strictly linear evolution, i.e., α ≃ 1, is favoured by these data, which is also in agreement with limits obtained from other independent cosmological tests. The dependence of the critical redshift z_m (at which a given angular size takes its minimal value) on the index α is briefly discussed.

We consider global monopoles in asymptotic de Sitter/anti-de Sitter spacetime. We present the asymptotic behaviour of the metric and Goldstone field function which is confirmed by our numerical analysis. We find that the appearance of horizons in this model depends strongly on the sign and value of the cosmological constant, as well as on the value of the gravitational coupling. In anti-de Sitter space, we find that for a fixed value of the cosmological constant, global monopoles without horizons exist only up to a critical value of the gravitational coupling. Moreover, we observe (in contrast to another recent study) that the introduction of a cosmological constant cannot render a positive mass of the global monopole.

Since the scalar-tensor theory of gravitation was proposed almost 50 years ago, it has recently become a robust alternative theory to Einstein's general relativity due to the fact that it appears to represent the lower level of a more fundamental theory and can serve both as a phenomenological theory to explain the recently observed acceleration of the universe, and to solve the cosmological constant problem. To my knowledge The Scalar-Tensor Theory of Gravitation by Y Fujii and K Maeda is the first book to develop a modern view on this topic and is one of the latest titles in the well-presented Cambridge Monographs on Mathematical Physics series.

This book is an excellent readable introduction and up-to-date review of the subject. The discussion is well organized; after a comprehensible introduction to the Brans-Dicke theory and the important role played by conformal transformations, the authors review cosmologies with the cosmological constant and how the scalar-tensor theory can serve to explain the accelerating universe, including discussions on dark energy, quintessence and braneworld cosmologies. The book ends with a chapter devoted to quantum effects. To make easy the lectures of the book, each chapter starts with a summary of the subject to be dealt with. As the book proceeds, important issues like conformal frames and the weak equivalence principle are fully discussed. As the authors warn in the preface, the book is not encyclopedic (from my point of view the list of references is fairly short, for example, but this is a minor drawback) and the choice of included topics corresponds to the authors' interests. Nevertheless, the book seems to cover a broad range of the most essential aspects of the subject. Long and 'boring' mathematical derivations are left to appendices so as not to interrupt the flow of the reasoning, allowing the reader to focus on the physical aspects of each subject. These appendices are a valuable help in entering into the mathematical details.

The intended audience is graduate students and the book is in fact well suited to a graduate course (the way in which the book is arranged and the subjects are presented is very pedagogical). However, it is as well a very good book for researchers in cosmology and gravitation, who will find much material of interest. I am sure this book will recieve wide acceptance from researchers interested in this field.

J Ibánez

To a relativist, a time period equivalent to that of 60 orbits of the Earth around the Sun, or 5.676438379482·10¹⁹ cm of proper time, may not sound particularly significant. Yet, in our human society, it gives us the opportunity of honouring those we love and respect. Such was the occasion for the publication of this volume in honour of Professor Jiri Bicák of the Institute of Theoretical Physics at Charles University in Prague - a city in which Tycho Brahe and Kepler worked together, and where Einstein struggled to construct his general theory of relativity.

An appropriate, but unusual, celebratory event which was organized on the relevant January evening involved an intersection of interesting time-shifted worldlines. A record of this is available at http://astro.troja.mff.cuni.cz/bicak/, which may help in comprehending the preface. Our purpose here, however, is to comment on the more permanent item that was produced for the occasion.

It must immediately be stated that this is not a typical festschrift in which leading authorities around the world contribute articles dedicated to an academic colleague. It was a surprise present from past research students to their teacher. It maintains the character of a personal tribute but, basically, the contributions are research papers of the highest quality. The result is a very valuable academic reference. As Bicák would have wanted, this is a substantial contribution to objective science, not a piece of post-modern sentimentalism.

Reflecting Bicák's own wide interests, the different contributions to this volume cover specific topics in general relativity, astrophysics, theoretical physics and cosmology. They include original articles and thorough up-to-date reviews. In all cases, detailed mathematical or computational analysis is guided by requirements of physical significance.

The first paper is by Dolezel on observations from within slowly rotating voids in cosmological models and their compatibility with Mach's principle. Stuchlik has thoroughly reviewed the effect of a small cosmological constant on geodesic motion and the equipotential surfaces associated with the formation of accretion discs, and Karas, Subr and Slechta report some interesting results from their model for analysing the dynamics of a stellar cluster near a galactic centre with an accretion disc. Semerák has contributed a thorough and most useful review of exact models for realistic axially symmetric discs of matter around rotating spheroidal black holes. There is a paper by Hledik illustrating the use of optical reference geometry and embedding diagrams for analysing the properties of orbits about black holes, and Ledvinka has illustrated graphically what a rotating neutron star would actually look like to an observer. Podolsky has comprehensively reviewed exact expanding and non-expanding impulsive gravitational waves, describing the various ways they may be constructed and their global properties in Minkowski, de Sitter and anti-de Sitter backgrounds. The spinning C-metric is investigated by Pravda and Pravdová with a view to clarifying its physical interpretation as a pair of accelerating Kerr black holes, and Balek has described the properties of spacetimes that can be constructed by cutting and pasting parts of Minkowski space. The volume concludes with some remarks by Kopf on a functional approach to the renormalization of the stress-energy tensor in the semiclassical Einstein equations, and a review by Krtous of boundary quantum mechanics in which measurements at the initial and final moments in time are treated independently and which can be formulated without reference to causal structure. These are all valuable articles which deserve to be widely known.

Overall, this is a most impressive tribute to a leader in the academic study of gravitation, who has clearly inspired the generation after him and helped establish a thriving research community in his beautiful native city.

Jerry Griffiths

The gravitational N-body problem is to describe the evolution of an isolated system of N point masses interacting only through Newtonian gravitational forces. For N =2 the solution is due to Newton. For N =3 there is no general analytic solution, but the problem has occupied generations of illustrious physicists and mathematicians including Laplace, Lagrange, Gauss and Poincaré, and inspired the modern subjects of nonlinear dynamics and chaos theory. The general gravitational N-body problem remains one of the oldest unsolved problems in physics.

Many-body problems can be simpler than few-body problems, and many physicists have attempted to apply the methods of classical equilibrium statistical mechanics to the gravitational N-body problem for N ≫ 1. These applications have had only limited success, partly because the gravitational force is too strong at both small scales (the interparticle potential energy diverges) and large scales (energy is not extensive). Nevertheless, we now understand a rich variety of behaviour in large-N gravitating systems. These include the negative heat capacity of isolated, gravitationally bound systems, which is the basic reason why nuclear burning in the Sun is stable; Antonov's discovery that an isothermal, self-gravitating gas in a container is located at a saddle point, rather than a maximum, of the entropy when the gas is sufficiently dense and hence is unstable (the 'gravothermal catastrophe'); the process of core collapse, in which relaxation induces a self-similar evolution of the central core of the system towards (formally) infinite density in a finite time; and the remarkable phenomenon of gravothermal oscillations, in which the central density undergoes periodic oscillations by factors of a thousand or more on the relaxation timescale - but only if N ≳ 10⁴.

The Gravitational Million-Body Problem is a monograph that describes our current understanding of the gravitational N-body problem. The authors have chosen to focus on N = 10⁶ for two main reasons: first, direct numerical integrations of N-body systems are beginning to approach this threshold, and second, globular star clusters provide remarkably accurate physical instantiations of the idealized N-body problem withN = 10⁵ – 10⁶.

The authors are distinguished contributors to the study of star-cluster dynamics and the gravitational N-body problem. The book contains lucid and concise descriptions of most of the important tools in the subject, with only a modest bias towards the authors' own interests. These tools include the two-body relaxation approximation, the Vlasov and Fokker-Planck equations, regularization of close encounters, conducting fluid models, Hill's approximation, Heggie's law for binary star evolution, symplectic integration algorithms, Liapunov exponents, and so on. The book also provides an up-to-date description of the principal processes that drive the evolution of idealized N-body systems - two-body relaxation, mass segregation, escape, core collapse and core bounce, binary star hardening, gravothermal oscillations - as well as additional processes such as stellar collisions and tidal shocks that affect real star clusters but not idealized N-body systems.

In a relatively short (300 pages plus appendices) book such as this, many topics have to be omitted. The reader who is hoping to learn about the phenomenology of star clusters will be disappointed, as the description of their properties is limited to only a page of text; there is also almost no discussion of other, equally interesting N-body systems such as galaxies(N ≈ 10⁶ – 10¹²), open clusters (N ≃ 10² – 10⁴), planetary systems, or the star clusters surrounding black holes that are found in the centres of most galaxies. All of these omissions are defensible decisions. Less defensible is the uneven set of references in the text; for example, nowhere is the reader informed that the classic predecessor to this work was Spitzer's 1987 monograph, Dynamical Evolution of Globular Clusters, or that the standard reference on the observational properties of stellar systems is Binney and Merrifield's Galactic Astronomy. A minor irritation is that many concepts are discussed several times before they are defined, and the index provides no pointer to the primary discussion; thus, for example, there are ten index entries for 'phase mixing' and no indication that the fourth of these refers to the actual definition.

The book is intended as a graduate textbook but more likely it will be used mainly in other contexts: by theoretical researchers, as an indispensable reference on the dynamics of gravitational N-body systems; by observational astronomers, as a readable summary of the theory of star cluster evolution; and by physicists seeking a well-written and accessible introduction to a simple problem that remains fascinating and incompletely understood after three centuries.

Scott Tremaine

Friday 19 September 2003

A production error has led to incorrect pagination of articles in Classical and Quantum Gravity, volume 20 (2003), issues 18–20. This temporary problem affected only the online journal and has now been corrected.

Articles published online in issue 18 showed duplicated page numbers with the earlier issue 16. These articles have been re-paginated online, as have articles in the following issues 19 and 20. The incorrect pages were:

Issue 18: L217–222, 3533–3812 Issue 19: L223–230, 3813–4008 Issue 20: L231–244, 4009–4180

and have been corrected to:

Issue 18: L225–230, 3855–4134 Issue 19: L231–238, 4135–4330 Issue 20: L239–252, 4331–4502.

As you may be aware, Institute of Physics Publishing has adopted incremental publishing and so further articles will be added to issue 20 before it is closed.

The re-pagination includes new tables of contents, abstracts, full-text PDF and bibliographic files. The printed journal was not affected and all copies have the correct page numbers.

If you downloaded any data from issues 18–20 of Classical and Quantum Gravity prior to Friday 19 September 2003, then we ask that you remove these files from your system and replace them with the new files from www.iop.org/journals/cqg. This is important for readers who have, for example, downloaded PDF files, saved bibliographic data or used the 'Recommend This Article' feature. Organizations that receive automatic data from Institute of Physics Publishing via our STACKS^TM service have been sent additional advice.

We apologise for the inconvenience caused by these corrections. Please contact us at cqg@iop.org if you have any queries.

Andrew Wray Senior Publisher, Classical and Quantum Gravity