Table of contents

We reduce the Boyer–Finley equation to a family of compatible systems of hydrodynamic type, with characteristic speeds expressed in terms of spaces of rational functions. The systems of hydrodynamic type are then solved by the generalized hodograph method, providing solutions of the Boyer–Finley equation containing functional parameters.

We show a global existence theorem for the Einstein-matter equations of T³-Gowdy symmetric spacetimes with stringy matter. The areal time coordinate is used. It is shown that this spacetime has a crushing singularity into the past. From these results we can show that the spacetime is foliated by compact hypersurfaces of constant mean curvature.

We describe the asymptotic boundary of the general homogeneous plane wave spacetime, using a construction of the 'points at infinity' from the causal structure of the spacetime as introduced by Geroch, Kronheimer and Penrose. We show that this construction agrees with the conformal boundary obtained by Berenstein and Nastase for the maximally supersymmetric ten-dimensional plane wave. We see in detail how the possibility of going beyond (or around) infinity arises from the structure of light cones. We also discuss the extension of the construction to time-dependent plane wave solutions, focusing on the examples obtained from the Penrose limit of Dp-branes.

We complete the list of fluxbrane solutions in classical supergravities by introducing Melvin-type spacetimes supported by antisymmetric forms of rank D − 1 and their pseudoscalar duals. In IIB theory, these solutions belong to the same family as the 7-brane and D-instanton. In current notation, a fluxbrane supported by the D − 1 form is an F0 brane, its Euclidean continuation is a cylindrical background which 'interacts' with a pointlike instanton. The general F0 brane can have a transverse space S_k × R^(D−k−2) with 1 ≤ k ≤ D − 2. For k = 1 we find the complete solution containing four parameters, three of them associated with pointlike singularities on the Melvin-type background. The S-dual to the F0 brane in ten dimensions is the F8 fluxbrane of codimension one, or F-wall; similar fluxbranes exist in any dimension if an appropriate form field is present. F-walls contain naked singularities unless one introduces source branes. In such a way one obtains new braneworld-type solutions with two bulk scalar fields. Their relation to the supersymmetric braneworlds is discussed.

We study the dynamics of a spherically symmetric dust shell separating two spacetime domains, the interior one being a part of the de Sitter spacetime and the exterior one having the extremalReißner–Nordström geometry. Extending the ideas of previous works on the subject, we show that it is possible to determine the (metastable) WKB quantum states of this gravitational system.

A solution to Einstein's equations is presented which describes an inhomogeneous universe with anisotropic pressure in the Kantowski–Sachs family. The spacetime is composed of a series of spherical shells of dust particles which possess angular momentum within the shell. The solution is derived from a spherically symmetric spacetime with the same matter content by fixing the areal radius of each shell to be equal. The spacetime may be thought of as the surface of a cylinder, each circle z = constant of which represents a two-sphere. As time passes, the cylinder expands or collapses and the shells move relative to one another on the surface of the cylinder. The equation describing the relative motion of the matter shells reveals that the flux of the gravitational field is directed along the cylinder and alters the motion of the shells in a physically intuitive way.

Numerical studies of the gravitational collapse of a stiff (P = ρ) fluid have found the now-familiar critical phenomena, namely scaling of the black-hole mass with a critical exponent and continuous self-similarity at the threshold of black-hole formation. Using the equivalence of an irrotational stiff fluid to a massless scalar field, we construct the critical solution as a scalar field solution by making a self-similarity ansatz. We find evidence that this solution has exactly one growing perturbation mode; both the mode and the critical exponent, γ ≃ 0.94, derived from its eigenvalue agree with those measured in perfect fluid collapse simulations. We explain why this solution is seen as a critical solution in stiff fluid collapse but not in scalar field collapse, and conversely why the scalar field critical solution is not seen in stiff fluid collapse, even though the two systems are locally equivalent.

We show that all purely magnetic Petrov type D, irrotational, aligned perfect fluid spacetimes are locally rotationally symmetric class III by the Ellis classification. This result is combined with a similar theorem for purely magnetic Petrov type D, shear-free, aligned perfect fluid spacetimes. For all purely magnetic locally rotationally symmetric class III perfect fluid spacetimes the pressure and energy density are both expressed in terms of a single function (of the timelike coordinate only). Therefore, these expressions define, implicitly, a nonlinear barotropic equation of state on intervals of this single function where the energy conditions are satisfied. However, a general expression is obtained for which the pressure is explicitly written as a function of the energy density. It is shown that in the asymptotic limit of large pressure and energy density the ratio between the pressure and energy density approaches the value 1/5. The only member of these spacetimes with a linear barotropic equation of state and a homothetic vector field is the purely magnetic Collins–Stewart spacetime.

The causal structure of spacetime offers a natural notion of an opposite or orthogonal in the logical sense, where the opposite of a set is formed by all points non-timelike related with it. We show that for a general spacetime the algebra of subsets that arises from this negation operation is a complete orthomodular lattice, and thus has several of the properties characterizing the algebra of physical propositions in quantum mechanics. We think this lattice could be used to investigate the causal structure in an algebraic context. As a first step in this direction, we show that the causal lattice is, in addition, atomic, find its atoms, and give necessary and sufficient conditions for irreducibility.

The analysis of how a stochastic background of gravitational radiation interacts with a spherical detector is given in detail, which leads to explicit expressions for the system response functions, as well as for the cross-correlation matrix of different readout channels. It is shown that distinctive features of GW-induced random detector excitations, relative to locally generated noise, are, in practice, insufficient for separating the signal from the noise by means of a single sphere.

We propose a canonical description of the dynamics of quantum systems on a class of Robertson–Walker spacetimes. We show that the worldline of an observer in such spacetimes determines a unique orbit in the identity component SO₀(4, 1) of the local conformal group of the spacetime and that this orbit determines a unique transport on the spacetime. For a quantum system on the spacetime modelled by a net of local algebras, the associated dynamics is expressed via a suitable family of 'propagators'. In the best of situations, this dynamics is covariant, but more typically the dynamics will be 'quasi-covariant' in a sense we make precise. We then show, by using our technique of 'transplanting' states and nets of local algebras from de Sitter space to Robertson–Walker space, that there exist quantum systems on Robertson–Walker spaces with quasi-covariant dynamics. The transplanted state is locally passive, in an appropriate sense, with respect to this dynamics.

We study the consequences of the existence of spacelike Ricci inheritance vectors (SpRIVs) parallel to x^a for a model of string cloud and string fluid stress tensor in the context of general relativity. Necessary and sufficient conditions are derived for a spacetime with a model of string cloud and string fluid stress tensor to admit a SpRIV, and a SpRIV which is also a spacelike conformal Killing vector. Also, some results are obtained.

This paper studies nonlinear deformations of the linear gauge theory of any number of spin-2 and spin-3/2 fields with general formal multiplication rules in place of standard Grassmann rules for manipulating the fields, in four spacetime dimensions. General possibilities for multiplication rules and coupling constants are simultaneously accommodated by regarding the set of fields equivalently as a single algebra-valued spin-2 field and single algebra-valued spin-3/2 field, where the underlying algebra is factorized into a field-coupling part and an internal multiplication part. The condition that there exists a gauge-invariant Lagrangian (to within a divergence) for these algebra-valued fields is used to derive determining equations whose solutions give all allowed deformation terms, yielding nonlinear field equations and non-Abelian gauge symmetries, together with all allowed formal multiplication rules as needed in the Lagrangian for the demonstration of invariance under the gauge symmetries and for the derivation of the field equations. In the case of spin-2 fields alone, the main result of this analysis is that all deformations (without any higher derivatives than those that appear in the linear theory) are equivalent to an algebra-valued Einstein gravity theory. By a systematic examination of factorizations of the algebra, a novel type of nonlinear gauge theory of two or more spin-2 fields is found, where the coupling for the fields is based on structure constants of an anticommutative, anti-associative algebra, and with formal multiplication rules that make the fields anticommuting (while products obey anti-associativity). Supersymmetric extensions of these results are obtained in the more general case when spin-3/2 fields are included.

In this paper, we prove that all five-dimensional axisymmetric Kaluza–Klein spacetime solutions with electrostatic fields may also be those of low-energy string theory. From the class of TS-like solutions in Kaluza–Klein theory we obtain the corresponding class of solutions with electric dipoles in low-energy string theory, which are enlarged to solutions with electric charges under the SO(1, 1) transformation. We obtain the complete metric for the TS-like solution with δ = 1. Lastly, we give a discussion.

A superembedding construction of general non-Abelian Born–Infeld actions in three dimensions is described. These actions have rigid target space and local worldvolume supersymmetry (i.e., kappa symmetry). The standard Abelian Born–Infeld gauge multiplet is augmented with an additional worldvolume SU(N) gauge supermultiplet. It is shown how to construct single-trace actions and in particular a kappa-supersymmetric extension of the symmetrized trace action.

The Riemannian 10j symbols are spin networks that assign an amplitude to each 4-simplex in the Barrett–Crane model of Riemannian quantum gravity. This amplitude is a function of the areas of the ten faces of the 4-simplex, and Barrett and Williams have shown that one contribution to its asymptotics comes from the Regge action for all non-degenerate 4-simplices with the specified face areas. However, we show numerically that the dominant contribution comes from degenerate 4-simplices. As a consequence, one can compute the asymptotics of the Riemannian 10j symbols by evaluating a 'degenerate spin network', where the rotation group SO(4) is replaced by the Euclidean group of isometries of ³. We conjecture formulae for the asymptotics of a large class of Riemannian and Lorentzian spin networks in terms of these degenerate spin networks, and check these formulae in some special cases. Among other things, this conjecture implies that the Lorentzian 10j symbols are asymptotic to 1/16 times the Riemannian ones.

(a) On page 4087, the first term in equation (3), Φ, should read □ Φ.

(b) On page 4087, in the paragraph below equation (3), Φ = ··· should read □ Φ = ···.

(c) On page 4087, the first term in equation (6), Φ, should read □ Φ.

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