Electric and magnetic Weyl tensors in higher dimensions

Recent results on purely electric (PE) or magnetic (PM) spacetimes in n dimensions are summarized. These include: Weyl types; diagonalizability; conditions under which direct (or warped) products are PE/PM.Comment: 4 pages; short summary of (parts of) arXiv:1203.3563. Proceedings of "Relativity and Gravitation - 100 Years after Einstein in Prague", Prague, June 25-29, 2012 (http://ae100prg.mff.cuni.cz/

Note on the invariant classification of vacuum type D spacetimes

We illustrate the fact that the class of vacuum type D spacetimes which are $\mathcal{I}$-\emph{non-degenerate} are invariantly classified by their scalar polynomial curvature invariants

SO(n + 1) Symmetric Solutions of the Einstein Equations in Higher Dimensions

A method of solving the Einstein equations with a scalar field is presented. It is applied to find higher dimensional vacuum metrics invariant under the group SO(n + 1) acting on n-dimensional spheres.Comment: 11 page

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

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

Bianchi identities in higher dimensions

A higher dimensional frame formalism is developed in order to study implications of the Bianchi identities for the Weyl tensor in vacuum spacetimes of the algebraic types III and N in arbitrary dimension $n$. It follows that the principal null congruence is geodesic and expands isotropically in two dimensions and does not expand in $n-4$ spacelike dimensions or does not expand at all. It is shown that the existence of such principal geodesic null congruence in vacuum (together with an additional condition on twist) implies an algebraically special spacetime. We also use the Myers-Perry metric as an explicit example of a vacuum type D spacetime to show that principal geodesic null congruences in vacuum type D spacetimes do not share this property.Comment: 25 pages, v3: Corrections to Appendix B as given in Erratum-ibid.24:1691,2007 are now incorporated (A factor of 2 was missing in certain Bianchi equations.

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