General Kundt spacetimes in higher dimensions

We investigate a general metric of the Kundt class of spacetimes in higher dimensions. Geometrically, it admits a non-twisting, non-shearing and non-expanding geodesic null congruence. We calculate all components of the curvature and Ricci tensors, without assuming any specific matter content, and discuss algebraic types and main geometric constraints imposed by general Einstein's field equations. We explicitly derive Einstein-Maxwell equations, including an arbitrary cosmological constant, in the case of vacuum or possibly an aligned electromagnetic field. Finally, we introduce canonical subclasses of the Kundt family and we identify the most important special cases, namely generalised pp-waves, VSI or CSI spacetimes, and gyratons.Comment: 15 page

Ricci identities in higher dimensions

We explore connections between geometrical properties of null congruences and the algebraic structure of the Weyl tensor in n>4 spacetime dimensions. First, we present the full set of Ricci identities on a suitable "null" frame, thus completing the extension of the Newman-Penrose formalism to higher dimensions. Then we specialize to geodetic null congruences and study specific consequences of the Sachs equations. These imply, for example, that Kundt spacetimes are of type II or more special (like for n=4) and that for odd n a twisting geodetic WAND must also be shearing (in contrast to the case n=4).Comment: 8 pages. v2: typo corrected between Propositions 2 and 3. v3: typo in the last term in the first line of (11f) corrected, missing term on the r.h.s. of (11p) added, first sentence between Propositions 2 and 3 slightly change

Cosmic No Hair for Collapsing Universes

It is shown that all contracting, spatially homogeneous, orthogonal Bianchi cosmologies that are sourced by an ultra-stiff fluid with an arbitrary and, in general, varying equation of state asymptote to the spatially flat and isotropic universe in the neighbourhood of the big crunch singularity. This result is employed to investigate the asymptotic dynamics of a collapsing Bianchi type IX universe sourced by a scalar field rolling down a steep, negative exponential potential. A toroidally compactified version of M*-theory that leads to such a potential is discussed and it is shown that the isotropic attractor solution for a collapsing Bianchi type IX universe is supersymmetric when interpreted in an eleven-dimensional context.Comment: Extended discussion to include Kantowski-Sachs universe. In press, Classical and Quantum Gravit

G_2 Perfect-Fluid Cosmologies with a proper conformal Killing vector

We study the Einstein field equations for spacetimes admitting a maximal two-dimensional abelian group of isometries acting orthogonally transitively on spacelike surfaces and, in addition, with at least one conformal Killing vector. The three-dimensional conformal group is restricted to the case when the two-dimensional abelian isometry subalgebra is an ideal and it is also assumed to act on non-null hypersurfaces (both, spacelike and timelike cases are studied). We consider both, diagonal and non-diagonal metrics and find all the perfect-fluid solutions under these assumptions (except those already known). We find four families of solutions, each one containing arbitrary parameters for which no differential equations remain to be integrated. We write the line-elements in a simplified form and perform a detailed study for each of these solutions, giving the kinematical quantities of the fluid velocity vector, the energy-density and pressure, values of the parameters for which the energy conditions are fulfilled everywhere, the Petrov type, the singularities in the spacetimes and the Friedmann-Lemaitre-Robertson-Walker metrics contained in each family.Comment: Latex, no figure

Properties of kinematic singularities

The locally rotationally symmetric tilted perfect fluid Bianchi type V cosmological model provides examples of future geodesically complete spacetimes that admit a `kinematic singularity' at which the fluid congruence is inextendible but all frame components of the Weyl and Ricci tensors remain bounded. We show that for any positive integer n there are examples of Bianchi type V spacetimes admitting a kinematic singularity such that the covariant derivatives of the Weyl and Ricci tensors up to the n-th order also stay bounded. We briefly discuss singularities in classical spacetimes.Comment: 13 pages. Published version. One sentence from version 2 correcte

Higher dimensional VSI spacetimes

We present the explicit metric forms for higher dimensional vanishing scalar invariant (VSI) Lorentzian spacetimes. We note that all of the VSI spacetimes belong to the higher dimensional Kundt class. We determine all of the VSI spacetimes which admit a covariantly constant null vector, and we note that in general in higher dimensions these spacetimes are of Ricci type III and Weyl type III. The Ricci type N subclass is related to the chiral null models and includes the relativistic gyratons and the higher dimensional pp-wave spacetimes. The spacetimes under investigation are of particular interest since they are solutions of supergravity or superstring theory.Comment: 14 pages, changes in second paragraph of the discussio

Qualitative Analysis of Causal Anisotropic Viscous Fluid Cosmological Models

The truncated Israel-Stewart theory of irreversible thermodynamics is used to describe the bulk viscous pressure and the anisotropic stress in a class of spatially homogeneous viscous fluid cosmological models. The governing system of differential equations is written in terms of dimensionless variables and a set of dimensionless equations of state is utilized to complete the system. The resulting dynamical system is then analyzed using standard geometric techniques. It is found that the presence of anisotropic stress plays a dominant role in the evolution of the anisotropic models. In particular, in the case of the Bianchi type I models it is found that anisotropic stress leads to models that violate the weak energy condition and to the creation of a periodic orbit in some instances. The stability of the isotropic singular points is analyzed in the case with zero heat conduction; it is found that there are ranges of parameter values such that there exists an attracting isotropic Friedmann-Robertson-Walker model. In the case of zero anisotropic stress but with non-zero heat conduction the stability of the singular points is found to be the same as in the corresponding case with zero heat conduction; hence the presence of heat conduction does not apparently affect the global dynamics of the model.Comment: 35 pages, REVTeX, 3 Encapsulated PostScript Figure

Kinematic Self-Similar Plane Symmetric Solutions

This paper is devoted to classify the most general plane symmetric spacetimes according to kinematic self-similar perfect fluid and dust solutions. We provide a classification of the kinematic self-similarity of the first, second, zeroth and infinite kinds with different equations of state, where the self-similar vector is not only tilted but also orthogonal and parallel to the fluid flow. This scheme of classification yields twenty four plane symmetric kinematic self-similar solutions. Some of these solutions turn out to be vacuum. These solutions can be matched with the already classified plane symmetric solutions under particular coordinate transformations. As a result, these reduce to sixteen independent plane symmetric kinematic self-similar solutions.Comment: 29 pages, accepted for publication in Classical Quantum Gravit

On higher dimensional Einstein spacetimes with a warped extra dimension

We study a class of higher dimensional warped Einstein spacetimes with one extra dimension. These were originally identified by Brinkmann as those Einstein spacetimes that can be mapped conformally on other Einstein spacetimes, and have subsequently appeared in various contexts to describe, e.g., different braneworld models or warped black strings. After clarifying the relation between the general Brinkmann metric and other more specific coordinate systems, we analyze the algebraic type of the Weyl tensor of the solutions. In particular, we describe the relation between Weyl aligned null directions (WANDs) of the lower dimensional Einstein slices and of the full spacetime, which in some cases can be algebraically more special. Possible spacetime singularities introduced by the warp factor are determined via a study of scalar curvature invariants and of Weyl components measured by geodetic observers. Finally, we illustrate how Brinkmann's metric can be employed to generate new solutions by presenting the metric of spinning and accelerating black strings in five dimensional anti-de Sitter space.Comment: 14 pages, minor changes in the text, mainly in Section 2.

Self-similar Bianchi type VIII and IX models

It is shown that in transitively self-similar spatially homogeneous tilted perfect fluid models the symmetry vector is not normal to the surfaces of spatial homogeneity. A direct consequence of this result is that there are no self-similar Bianchi VIII and IX tilted perfect fluid models. Furthermore the most general Bianchi VIII and IX spacetime which admit a four dimensional group of homotheties is given.Comment: 5 pages, Latex; One reference and minor clarifications added. To appear in General Relativity and Gravitatio