Table of contents

A manifestly gauge-invariant formulation of the coupling of the Maxwell theory with an Einstein-Cartan geometry is given, where the spacetime torsion originates from a massless Kalb-Ramond field augmented by suitable U(1) Chern-Simons terms. We focus on the situation where the torsion violates parity, and relate it to earlier proposals for gravitational parity violation.

Gravitational waves emitted by perturbed black holes or relativistic stars are dominated by `quasinormal ringing', damped oscillations at single frequencies which are characteristic of the underlying system. These quasinormal modes have been studied for a long time, often with the intent of describing the time evolution of a perturbation in terms of these modes in a way very similar to a normal-mode analysis. In this review, we summarize how quasinormal modes are defined and computed. We will see why they have been regarded as closely analogous to normal modes, and discover why they are actually quite different. We also discuss how quasinormal modes can be used in the analysis of a gravitational wave signal, such as will hopefully be detected in the near future.

A specific choice of gauge is shown to imply a decoupling between the tensor and scalar components of gravitational radiation in the context of Brans-Dicke-type theories of gravitation. The comparison of the predictions of these theories with those of general relativity is thereby made straightforward.

We demonstrate that the high isotropy of the cosmic microwave background (CMB), combined with the Copernican principle, is not sufficient to prove homogeneity of the universe - in contrast to previous results on this subject. The crucial additional factor not included in earlier work is the acceleration of the fundamental observers. We find the complete class of irrotational perfect fluid spacetimes admitting an exactly isotropic radiation field for every fundamental observer and show that they are Friedmann-Lemaître-Robertson-Walker (FLRW) if and only if the acceleration is zero. While inhomogeneous in general, these spacetimes all possess three-dimensional symmetry groups, from which it follows that they also admit a thermodynamic interpretation.

In addition to perfect fluids models we also consider multi-component fluids containing non-interacting radiation, dust and a quintessential scalar field or cosmological constant in which the radiation is isotropic for the geodesic (dust) observers. It is shown that the non-acceleration of the fundamental observers forces these spacetimes to be FLRW.

While it is plausible that fundamental observers (galaxies) in the real universe follow geodesics, it is strictly necessary to determine this from local observations for the cosmological principle to be more than an assumption. We discuss how observations may be used to test this.

The asymptotic behaviour at late times of inhomogeneous axion-dilaton cosmologies is investigated. The spacetimes considered here admit two Abelian spacelike Killing vectors. These spacetimes evolve towards an anisotropic universe containing gravitational radiation. Furthermore, a peeling-off behaviour of the Weyl tensor and the antisymmetric tensor field strength is found. The relation to the pre-big-bang scenario is briefly discussed.

Quantization in the minisuperspace of non-minimal scalar-tensor theories leads to a partial differential equation which is non-separable. Through a conformal transformation we can recast the Wheeler-DeWitt equation in an integrable form, which corresponds to the minimal coupling case, whose general solution is known. Performing the inverse conformal transformation in the solution thus found, we can construct the corresponding solution in the original frame. This procedure can also be employed with the Bohmian trajectories. In this way, we can study the classical limit of some particular solutions of this quantum model. While the classical limit of these solutions occurs for small scale factors in the Einstein frame, it happens for small values of the scalar field non-minimally coupled to gravity in the Jordan frame, which includes large scale factors.

Geometric features (including convexity properties) of an exact interior gravitational field due to a self-gravitating axisymmetric body of perfect fluid in stationary, rigid rotation are studied. In spite of the seemingly non-Newtonian features of the bounding surface for some rotation rates, we show, by means of a detailed analysis of the three-dimensional spatial geodesics, that the standard Newtonian convexity properties do hold. A central role is played by a family of geodesics that are introduced here, and provide a generalization of the Newtonian straight lines parallel to the axis of rotation.

We evoke situations where large fluctuations in the entropy are induced, our main example being a spacetime containing a potential black hole whose formation depends on the outcome of a quantum mechanical event. We argue that the teleological character of the event horizon implies that the consequent entropy fluctuations must be taken seriously in any interpretation of the quantal formalism. We then indicate how the entropy can be well defined despite the teleological character of the horizon, and we argue that this is possible only in the context of a spacetime or `histories' formulation of quantum gravity, as opposed to a canonical one, concluding that only a spacetime formulation has the potential to compute - from first principles and in the general case - the entropy of a black hole. From the entropy fluctuations in a related example, we also derive a condition governing the form taken by the entropy, when it is expressed as a function of the quantal density operator.

Inspired by the spin geometry theorem, two operators are defined which measure angles in the quantum theory of geometry. One operator assigns a discrete angle to every pair of surfaces passing through a single vertex of a spin network. This operator, which is effectively the cosine of an angle, is defined via a scalar product density operator and the area operator. The second operator assigns an angle to two `bundles' of edges incident to a single vertex. While somewhat more complicated than the earlier geometric operators, there are a number of properties that are investigated including the full spectrum of several operators and, using results of the spin geometry theorem, conditions to ensure that semiclassical geometry states replicate classical angles.

We compute mass outflow rates from accretion discs around compact objects, such as neutron stars and black holes. These computations are done using combinations of exact transonic inflow and outflow solutions which may or may not form standing shock waves. Assuming that the bulk of the outflow is from the effective boundary layers of these objects, we find that the ratio of the outflow and inflow rates varies anywhere from a few per cent to even close to a 100% (i.e. close to the disc evacuation case) depending on the initial parameters of the disc, the degree of compression of matter near the centrifugal barrier, and the polytropic index of the flow. Our result, in general, matches the outflow rates obtained through a fully time-dependent numerical simulation. In some region of the parameter space when the standing shock does not form, our results indicate that the disc may be evacuated and may produce quiescence states.

Some exact solutions in the Brans-Dicke (BD) theory are shown for a Bianchi V metric having the properties of inflationary expansion, graceful exit and asymptotic evolution to a Friedmann-Robertson-Walker open model. It is remarkable that inflationary behaviour can occur, even without a cosmological potential or constant. However, the horizon and flatness problems cannot be solved within the standard BD theory because the inflationary period is severely restricted by the value of the BD parameter .

We extend our analysis for scalar fields in a Robertson-Walker metric to the electromagnetic and Dirac fields by the method of invariants. The issue of the relation between conformal properties and particle production is re-examined and it is verified that the electromagnetic and massless spinor actions are conformal invariant, while the massless conformally coupled scalar field is not. For the scalar field case it is pointed out that the violation of conformal symmetry due to surface terms, although not influential for the equations of motion, does lead to effects in the quantized theory.

We calculate the quantum corrections of geometric and thermodynamic quantities for the Reissner-Nordström charged black hole, within the context of the two-dimensional spherically symmetric dilaton gravity model. Special attention is paid to the quantum corrections of the extreme Reissner-Nordström solution. We find a state of the extreme black hole with regular behaviour on the horizon.

Sound wave propagation in a relativistic perfect fluid with a non-homogeneous isentropic flow is studied in terms of acoustic geometry. The sound wave equation turns out to be equivalent to the equation of motion for a massless scalar field propagating in a curved spacetime geometry. The geometry is described by the acoustic metric tensor which depends locally on the equation of state and the 4-velocity of the fluid. For a relativistic supersonic flow in curved spacetime the ergosphere and acoustic horizon may be defined in a way analogous to the non-relativistic case. A general-relativistic expression for the acoustic analogue of surface gravity has been found.

The null geodesic equations in the Alcubierre warp-drive spacetime are numerically integrated to determine the angular deflection and redshift of photons which propagate through the distortion of the `warp-drive' bubble to reach an observer at the origin of the warp effect. We find that for a starship with an effective warp speed exceeding the speed of light, stars in the forward hemisphere will appear closer to the direction of motion than they would to an observer at rest. This aberration is qualitatively similar to that caused by special relativity. Behind the starship, a conical region forms from within which no signal can reach the starship, an effective `horizon'. Conversely, there is also a horizon-like structure in a conical region in front of the starship, into which the starship cannot send a signal. These causal structures are somewhat analogous to the Mach cones associated with supersonic fluid flow.

I show how a minor modification of the Alcubierre geometry can dramatically improve the total energy requirements for a `warp bubble' that can be used to transport macroscopic objects. A spacetime is presented for which the total negative mass needed is of the order of a few solar masses, accompanied by a comparable amount of positive energy. This puts the warp drive in the mass scale of large traversable wormholes. The new geometry satisfies the quantum inequality concerning WEC violations and has the same advantages as the original Alcubierre spacetime.

Exact solutions of Einstein's equations are obtained for a massless dilaton field interacting with an electromagnetic field coupled with gravity in Bianchi I, III and Kantowski-Sachs models, and corresponding properties of the spacetime are discussed.

We propose a method to construct a quantum theory of matter fields in a topology-changing universe. Analytic continuation of the semiclassical gravity of a Lorentzian geometry leads to a non-unitary Schrödinger equation in a Euclidean region of spacetime, which does not have a direct interpretation as a quantum theory of the Minkowski spacetime. In this Euclidean region we quantize the Euclidean geometry, derive the time-dependent Schrödinger equation and find the quantum states using the Liouville-Neumann method. The Wick rotation of these quantum states provides the correct Hilbert space of the matter field in the Euclidean region of the Lorentzian geometry. It is found that the direct quantization of a scalar field in the Lorentzian geometry involves an unusual commutation rule in the Euclidean region. Finally, we discuss the interpretation of the periodic solution of the semiclassical gravity equation in the Euclidean geometry as a finite-temperature solution for the gravity-matter system in the Lorentzian geometry.

Recent work in the literature has proposed the use of non-local boundary conditions in Euclidean quantum gravity. The present paper studies first a more general form of such a scheme for bosonic gauge theories, by adding to the boundary operator for mixed boundary conditions of local nature a 2 × 2 matrix of pseudo-differential operators with pseudo-homogeneous kernels. The requirement of invariance of such boundary conditions under infinitesimal gauge transformations leads to non-local boundary conditions on ghost fields. In Euclidean quantum gravity, an alternative scheme is proposed, where non-local boundary conditions and the requirement of their complete gauge invariance are sufficient to lead to gauge-field and ghost operators of pseudo-differential nature. The resulting boundary conditions have a Dirichlet and a pseudo-differential sector, and are pure Dirichlet for the ghost. This approach is eventually extended to Euclidean Maxwell theory.

We perform the gauge-fixing of the theory of a chiral 2-form boson in six dimensions starting from the action given by Pasti, Sorokin and Tonin. We use the Batalin-Vilkovisky formalism, introducing antifields and writing down an extended action satisfying the classical master equation. Then we gauge-fix the three local symmetries of the extended action in two different ways.

Conformastationary metrics - those of the form

have been derived by Perjes and by Israel and Wilson as source-free solutions of the Einstein-Maxwell equations. By analogy with the conformastatic metrics which have charged dust sources it was assumed that conformastationary metrics would be the external metrics of charged dust in steady motion. However, for axially symmetric conformastationary metrics we show that, as well as moving dust, hoop tensions are always necessary to balance the centrifugal forces induced by the motion. Exact examples of conformastationary metrics with disc sources are worked out in full. Generalizations to non-axially symmetric conformastationary metrics are indicated.

We investigate in detail the qualitative behaviour of the class of Bianchi type B spatially homogeneous cosmological models in which the matter content is composed of two non-interacting components; the first component is described by a barotropic fluid having a gamma-law equation of state, whilst the second is a non-interacting scalar field with an exponential potential V() = e^k. In particular, we study the asymptotic properties of the models both at early and late times, paying particular attention to whether the models isotropize (and inflate) to the future, and we discuss the genericity of the cosmological scaling solutions.

In this work we calculate the low-energy effective action for gravity with torsion, obtained after the integration of scalar and fermionic matter fields, using the local momentum representation based on the Riemann normal coordinates expansion. By considering this expansion around different spacetime points, we also compute the non-local terms together with the more usual divergent ones. Finally, we discuss the applicability of our results to the calculation of particle production probabilities.

We consider the Taub metric and show there exist spacelike hypersurfaces where the electric part of the Weyl tensor vanishes while the magnetic part remains non-zero. One such hypersurface is re-embedded in a Taub-like spacetime. A suitable choice of the functions gives a two-parameter family of irrotational perfect fluid spacetimes. A hypersurface orthogonal observer in this spacetime measures the Weyl tensor to be purely magnetic.

The five-dimensional induced-matter theory is reformulated to describe matter and entropy creation in the very early Universe, in the presence of a variable speed of light and gravitational constant. The five-dimensional vacuum field equations induce a four-dimensional cosmological fluid with the particle creation rate being determined by the time variation rate of the metric tensor component of the fifth dimension. For a homogeneous and isotropic flat Friedmann-Robertson-Walker geometry exact analytical solutions of the five-dimensional gravitational field equations are obtained, leading to a self-consistent cosmological model describing matter and entropy generation from the extra dimensions.

This paper considers metrics whose curvature tensor makes sense as a distribution. A class of such metrics, the regular metrics, was defined and studied by Geroch and Traschen. Here, we generalize their definition to form a wider class: semi-regular metrics. We then examine in detail two metrics that are semi-regular but not regular: (a) Minkowski spacetime minus a wedge and (b) a certain travelling wave metric.

In numerically constructing a spacetime that has an approximate timelike Killing vector, it is useful to choose spacetime coordinates adapted to the symmetry, so that the metric and matter variables vary only slowly with time in these coordinates. In particular, this is a crucial issue in numerically calculating a binary black hole inspiral. An approximate homothetic vector plays a role in critical gravitational collapse. We summarize old and new suggestions for finding such coordinates from a general point of view. We then test some of these in various toy models with spherical symmetry, including critical fluid collapse and critical scalar field collapse.

A class of globally regular solutions of the Einstein-Maxwell equations is given whose exteriors are arbitrarily close to that of an extreme black hole.

In 2000, the frequency of Classical and Quantum Gravity (CQG) will rise from 12 to 24 issues. This change reflects the continued development of the journal. Over the past five years submissions to CQG have grown by 39%, while acceptances have risen by 25%. The difference between these figures reflects the increasingly high standards of peer review applied on the journal, the overall acceptance rate having fallen from 58% to 50%.

By making more space available, the publishers seek to significantly reduce acceptance-to-publication times. It is our aim to ensure that the content of CQG remains timely, without compromising the journal's rigorous peer-review procedure.

The electronic version of CQG will remain available to subscribers at no extra cost. The 2000 package will also include an extended full-text archive covering every issue of the journal from 1991 to 1999, together with a complete abstract archive. Users will also be able to use HyperCite^TM technology to link directly to the journals of the American Physical Society and the American Institute of Physics, as well as a range of other resources. The forthcoming volume of CQG will include two conference-based special issues, from STRINGS'99 and the International Symposium on Experimental Gravitation. With a number of high-profile research papers in the pipeline, the journal is set to begin the new century on impressive form.