2,021 research outputs found
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
Brane Waves
In brane-world cosmology gravitational waves can propagate in the higher
dimensions (i.e., in the `bulk'). In some appropriate regimes the bulk
gravitational waves may be approximated by plane waves. We systematically study
five-dimensional gravitational waves that are algebraically special and of type
N. In the most physically relevant case the projected non-local stress tensor
on the brane is formally equivalent to the energy-momentum tensor of a null
fluid. Some exact solutions are studied to illustrate the features of these
branes; in particular, we show explicity that any plane wave brane can be
embedded into a 5-dimensional Siklos spacetime. More importantly, it is
possible that in some appropriate regime the bulk can be approximated by
gravitational plane waves and thus may act as initial conditions for the
gravitational field in the bulk (thereby enabling the field equations to be
integrated on the brane).Comment: 9 pages v3:revised version, to appear in CQ
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 , , and at the present epoch. There are several theoretical suggestions for
the cosmological 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
(), and another perfect fluid, which is a mixture of
radiation and/or matter components with positive pressure (), which define the associated one-fluid model (). We introduce a useful classification which contains 4 classes of
models defined by the presence or absence of energy transfer and by the
stationarity ( and ) or/and non stationarity (
or time dependent) of the equations of state. It is shown that, for
given and , the energy transfer defines 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,
, and , 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
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
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
Qualitative Analysis of Early Universe Cosmologies
A qualitative analysis is presented for a class of homogeneous cosmologies
derived from the string effective action when a cosmological constant is
present in the matter sector of the theory. Such a term has significant effects
on the qualitative dynamics. For example, models exist which undergo a series
of oscillations between expanding and contracting phases due to the existence
of a heteroclinic cycle in the phase space. Particular analytical solutions
corresponding to the equilibrium points are also found.Comment: Submitted to Journal of Mathematical Physics, 18 pages, 4 figures,
uses package "graphicx" to insert figure
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
All metrics have curvature tensors characterised by its invariants as a limit: the \epsilon-property
We prove a generalisation of the -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
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
- …