Table of contents

The stationary gravitational field of two identical counter-moving beams of pure radiation is found in full generality. The solution depends on an arbitrary function and a parameter which sets the scale of the energy density. Some of its properties are studied. Previous particular solutions are derived as subcases.

We consider the dynamics of a viscous cosmological fluid in the generalized Randall–Sundrum model for an anisotropic, Bianchi type I brane. To describe the dissipative effects we use the Israel–Hiscock–Stewart full causal thermodynamic theory. By assuming that the matter on the brane obeys a barotropic linear equation of state, and that the bulk viscous pressure has a power-law dependence on the energy density, the general solution of the field equations can be obtained in an exact parametric form. The solutions obtained describe generally a non-inflationary braneworld. In the large time limit the brane universe isotropizes, ending in an isotropic and homogeneous state. The evolution of the temperature and the comoving entropy of the universe is also considered, and it is shown that due to viscous dissipative processes a large amount of entropy is created in the early stages of evolution of the braneworld.

We show that the spacetime of the near-horizon limit of the extreme rotating d = 5 black hole, which is maximally supersymmetric in N = 2, d = 5 supergravity for any value of the rotation parameter j ∊ [−1, 1], is locally isomorphic to a homogeneous non-symmetric spacetime corresponding to an element of the one-parameter family of coset spaces SO(2, 1) × SO(3)/SO(2)_j in which the subgroup SO(2)_j is a combination of the two SO(2) subgroups of SO(2, 1) and SO(3).

The contributions to the heat kernel coefficients generated by the corners of the boundary are studied. For this purpose the internal and external sectors of a wedge and a cone are considered. These sectors are obtained by introducing, inside the wedge, a cylindrical boundary. Transition to a cone is accomplished by identification of the wedge sides. The basic result of the paper is the calculation of the individual contributions to the heat kernel coefficients generated by the boundary singularities. In the course of this analysis certain patterns, that are followed by these contributions, are revealed. The implications of the obtained results in calculations of the vacuum energy for regions with nonsmooth boundary are discussed. The rules for obtaining all the heat kernel coefficients for the minus Laplace operator defined on a polygon or in its cylindrical generalization are formulated.

We study the motion of test particles and electromagnetic waves in the Kerr–Newman–Taub–NUT spacetime in order to elucidate some of the effects associated with the gravitomagnetic monopole moment of the source. In particular, we determine in the linear approximation the contribution of this monopole to the gravitational time delay and the rotation of the plane of the polarization of electromagnetic waves. Moreover, we consider 'spherical' orbits of uncharged test particles in the Kerr–Taub–NUT spacetime and discuss the modification of the Wilkins orbits due to the presence of the gravitomagnetic monopole.

We study the motion of a magnetized particle orbiting around a supermassive Schwarzschild black hole, surrounded by a strong (asymptotically uniform) magnetic field. Using the Hamilton–Jacobi formalism, we solve in a fully analytical way the problem of finding the innermost circular orbits. We show that, for suitable values of the parameters controlling the magnetic interaction, these orbits may become stable near r = 3M, hence giving rise to a possible mechanism for particle confinement and energy storage. We argue that any sudden change in the above parameters could allow for abrupt release of large amounts of energy from such innermost orbits.

We try to give hereafter an answer to some open questions about the definition of conserved quantities in Chern–Simons theory, with particular reference to Chern–Simons AdS₃ gravity. Our attention is focused on the problem of global covariance and gauge invariance of the variation of Noether charges. A theory which satisfies the principle of covariance on each step of its construction is developed, starting from a gauge invariant Chern–Simons Lagrangian and using a recipe developed by Allemandi et al (2002 Class. Quantum Grav.19 2633–55, 237–58) to calculate the variation of conserved quantities. The problem of giving a mathematical well-defined expression for the infinitesimal generators of symmetries is pointed out and it is shown that the generalized Kosmann lift of spacetime vector fields leads to the expected numerical values for the conserved quantities when the solution corresponds to the BTZ black hole. The fist law of black-hole mechanics for the BTZ solution is then proved and the transition between the variation of conserved quantities in Chern–Simons AdS₃ gravity theory and the variation of conserved quantities in general relativity is analysed in detail.

Whether a string has rotation and shear can be investigated by an analogy with a congruence of point particles. Rotation and shear involve first covariant spacetime derivatives of a vector field and, because the metric stress tensor for both the point particle and the string have no such derivatives, the best vector fields can be identified by requiring the conservation of metric stress. It is found that the best vector field is a non-unit accelerating field in x, rather than a unit non-accelerating vector involving the momenta; it is also found that there is an equation obeyed by the spacetime derivative of the Lagrangian using a notation which will be defined in the paper. The relationship between membranes and fluids is looked at, and it is shown how to produce a membrane with arbitrary Γ for the Γ-equation of state.

Isotropic cosmological singularities are singularities which can be removed by rescaling the metric. In some cases already studied, the existence and uniqueness of cosmological models with data at the singularity has been established (Anguige K and Tod K P 1999 Ann. Phys., NY276 257–93, 294–320, Anguige K 2000 Ann. Phys., NY285 395–419). These were cosmologies with, as source, either perfect fluids with linear equations of state or massless, collisionless particles. In this paper, we consider how to extend these results to a variety of other matter models. These are scalar fields, massive collisionless matter, the Yang–Mills plasma given by Choquet-Bruhat (Choquet-Bruhat Y 1996 Yang–Mills plasmas Global Structure and Evolution in General Relativity (Springer Lecture Notes in Physics vol 460) ed S Cotsakis and G W Gibbons (Berlin: Springer)) and matter satisfying the Einstein–Boltzmann equation.

An implicit fundamental assumption in relativistic perturbation theory is that there exists a parametric family of spacetimes that can be Taylor expanded around a background. The choice of the latter is crucial to obtain a manageable theory, so that it is sometime convenient to construct a perturbative formalism based on two (or more) parameters. The study of perturbations of rotating stars is a good example: in this case one can treat the stationary axisymmetric star using a slow rotation approximation (expansion in the angular velocity Ω), so that the background is spherical. Generic perturbations of the rotating star (say parametrized by λ) are then built on top of the axisymmetric perturbations in Ω. Clearly, any interesting physics requires nonlinear perturbations, as at least terms λΩ need to be considered. In this paper, we analyse the gauge dependence of nonlinear perturbations depending on two parameters, derive explicit higher-order gauge transformation rules and define gauge invariance. The formalism is completely general and can be used in different applications of general relativity or any other spacetime theory.

We present a quantum model for the motion of N point particles, implying nonlocal (i.e., superluminal) influences of external fields on the trajectories, that is nonetheless fully relativistic. In contrast to other models that have been proposed, this one involves no additional spacetime structure as would be provided by a (possibly dynamical) foliation of spacetime. This is achieved through the interplay of opposite microcausal and macrocausal (i.e., thermodynamic) arrows of time.

Operator L(ω) for spin 1/2 fields (see (6.8)-(6.10)) is Hermitian with respect to product (6.11) when parameter M defined in (6.1) is a constant. Equations (6.12), (6.13) and (6.16) should be considered for this case only.