A spacetime not characterised by its invariants is of aligned type II

By using invariant theory we show that a (higher-dimensional) Lorentzian metric that is not characterised by its invariants must be of aligned type II; i.e., there exists a frame such that all the curvature tensors are simultaneously of type II. This implies, using the boost-weight decomposition, that for such a metric there exists a frame such that all positive boost-weight components are zero. Indeed, we show a more general result, namely that any set of tensors which is not characterised by its invariants, must be of aligned type II. This result enables us to prove a number of related results, among them the algebraic VSI conjecture.Comment: 14pages, CQG to appea

Two-fluid matter-quintessence FLRW models: energy transfer and the equation of state of the universe

Recent observations support the view that the universe is described by a FLRW model with $\Omega_m^0 \approx 0.3$, $\Omega_{\Lambda}^0 \approx 0.7$, and $w \leq -1/3$ at the present epoch. There are several theoretical suggestions for the cosmological $\Lambda$ component and for the particular form of the energy transfer between this dark energy and matter. This gives a strong motive for a systematic study of general properties of two-fluid FLRW models. We consider a combination of one perfect fluid, which is quintessence with negative pressure ($p_Q = w\epsilon_Q$), and another perfect fluid, which is a mixture of radiation and/or matter components with positive pressure ($p = \beta \epsilon_m$), which define the associated one-fluid model ($p = \gamma \epsilon$). We introduce a useful classification which contains 4 classes of models defined by the presence or absence of energy transfer and by the stationarity ($w = const.$ and $\beta = const.$) or/and non stationarity ($w$ or $\beta$ time dependent) of the equations of state. It is shown that, for given $w$ and $\beta$, the energy transfer defines $\gamma$ and, therefore, the total gravitating mass and dynamics of the model. We study important examples of two-fluid FLRW models within the new classification. The behaviour of the energy content, gravitating mass, pressure, and the energy transfer are given as functions of the scale factor. We point out three characteristic scales, $a_E$, $a_{\cal P}$ and $a_{\cal M}$, which separate periods of time in which quintessence energy, pressure and gravitating mass dominate. Each sequence of the scales defines one of 6 evolution types

Medium and large-scale variations of dynamo-induced electric fields from AE ion drift measurements

Current models of the low latitude electric field are largely based on data from incoherent scatter radars. These observations are extended through the addition of the rather extensive high quality electric field measurements from the Ion Drift Meter (IDM) aboard the Atmosphere Explorer (AE) spacecraft. Some preliminary results obtained from the Unified Abstract files of satellite AE-E are presented. This satellite was active from the end of 1975 through June 1981 in various elliptical and circular orbits having an inclination near 20 deg. The resulting data can be examined for the variation of ion drift with latitude, longitude, season, solar cycle, altitude, and magnetic activity. The results presented deal primarily with latitudinal variations of the drift features. Diagrams of data are given and briefly interpreted. The preliminary results presented here indicate that IDM data from the AE and the more recent Dynamics Explorer B spacecraft should continue to disclose some interesting and previously unobserved dynamical features of the low latitude F region

Alignment and algebraically special tensors in Lorentzian geometry

We develop a dimension-independent theory of alignment in Lorentzian geometry, and apply it to the tensor classification problem for the Weyl and Ricci tensors. First, we show that the alignment condition is equivalent to the PND equation. In 4D, this recovers the usual Petrov types. For higher dimensions, we prove that, in general, a Weyl tensor does not possess aligned directions. We then go on to describe a number of additional algebraic types for the various alignment configurations. For the case of second-order symmetric (Ricci) tensors, we perform the classification by considering the geometric properties of the corresponding alignment variety.Comment: 19 pages. Revised presentatio

All metrics have curvature tensors characterised by its invariants as a limit: the \epsilon-property

We prove a generalisation of the $\epsilon$-property, namely that for any dimension and signature, a metric which is not characterised by its polynomial scalar curvature invariants, there is a frame such that the components of the curvature tensors can be arbitrary close to a certain "background". This "background" is defined by its curvature tensors: it is characterised by its curvature tensors and has the same polynomial curvature invariants as the original metric.Comment: 6 page

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

Late-time behaviour of the tilted Bianchi type VI−1/9_{-1/9} models

We study tilted perfect fluid cosmological models with a constant equation of state parameter in spatially homogeneous models of Bianchi type VI$_{-1/9}$ using dynamical systems methods and numerical simulations. We study models with and without vorticity, with an emphasis on their future asymptotic evolution. We show that for models with vorticity there exists, in a small region of parameter space, a closed curve acting as the attractor.Comment: 13 pages, 1 figure, v2: typos fixed, minor changes, matches published versio