294,439 research outputs found
On BEL-configurations and finite semifields
The BEL-construction for finite semifields was introduced in \cite{BEL2007};
a geometric method for constructing semifield spreads, using so-called
BEL-configurations in . In this paper we investigate this construction
in greater detail, and determine an explicit multiplication for the semifield
associated with a BEL-configuration in , extending the results from
\cite{BEL2007}, where this was obtained only for . Given a
BEL-configuration with associated semifields spread , we also show
how to find a BEL-configuration corresponding to the dual spread
. Furthermore, we study the effect of polarities in on
BEL-configurations, leading to a characterisation of BEL-configurations
associated to symplectic semifields.
We give precise conditions for when two BEL-configurations in
define isotopic semifields. We define operations which preserve the BEL
property, and show how non-isotopic semifields can be equivalent under this
operation. We also define an extension of the ```switching'' operation on
BEL-configurations in introduced in \cite{BEL2007}, which, together
with the transpose operation, leads to a group of order acting on
BEL-configurations
Obtaining the Weyl tensor from the Bel-Robinson tensor
The algebraic study of the Bel-Robinson tensor proposed and initiated in a
previous work (Gen. Relativ. Gravit. {\bf 41}, see ref [11]) is achieved. The
canonical form of the different algebraic types is obtained in terms of
Bel-Robinson eigen-tensors. An algorithmic determination of the Weyl tensor
from the Bel-Robinson tensor is presented.Comment: 21 page
Bel-Robinson tensor and dominant energy property in the Bianchi type I Universe
Within the framework of Bianchi type-I space-time we study the Bel-Robinson
tensor and its impact on the evolution of the Universe. We use different
definitions of the Bel-Robinson tensor existing in the literature and compare
the results. Finally we investigate the so called "dominant super-energy
property" for the Bel-Robinson tensor as a generalization of the usual dominant
energy condition for energy momentum tensors.
Keywords: Bianchi type I model, super-energy tensors
Pacs: 03.65.Pm and 04.20.HaComment: 15 pages, revised version, no figure
Dynamical laws of superenergy in General Relativity
The Bel and Bel-Robinson tensors were introduced nearly fifty years ago in an
attempt to generalize to gravitation the energy-momentum tensor of
electromagnetism. This generalization was successful from the mathematical
point of view because these tensors share mathematical properties which are
remarkably similar to those of the energy-momentum tensor of electromagnetism.
However, the physical role of these tensors in General Relativity has remained
obscure and no interpretation has achieved wide acceptance. In principle, they
cannot represent {\em energy} and the term {\em superenergy} has been coined
for the hypothetical physical magnitude lying behind them. In this work we try
to shed light on the true physical meaning of {\em superenergy} by following
the same procedure which enables us to give an interpretation of the
electromagnetic energy. This procedure consists in performing an orthogonal
splitting of the Bel and Bel-Robinson tensors and analysing the different parts
resulting from the splitting. In the electromagnetic case such splitting gives
rise to the electromagnetic {\em energy density}, the Poynting vector and the
electromagnetic stress tensor, each of them having a precise physical
interpretation which is deduced from the {\em dynamical laws} of
electromagnetism (Poynting theorem). The full orthogonal splitting of the Bel
and Bel-Robinson tensors is more complex but, as expected, similarities with
electromagnetism are present. Also the covariant divergence of the Bel tensor
is analogous to the covariant divergence of the electromagnetic energy-momentum
tensor and the orthogonal splitting of the former is found. The ensuing {\em
equations} are to the superenergy what the Poynting theorem is to
electromagnetism. See paper for full abstract.Comment: 27 pages, no figures. Typos corrected, section 9 suppressed and more
acknowledgments added. To appear in Classical and Quantum Gravit
The Velocity Field of Quasar Broad Emission Line Gas
In this Letter, the broad emission line (BEL) profiles of superluminal
quasars with apparent jet velocities, , (ultraluminal QSOs, or
ULQSOs hereafter) are studied as a diagnostic of the velocity field of the BEL
emitting gas in quasars. The ULQSOs are useful because they satisfy a very
strict kinematical constraint, their parsec scale jets must be propagating
within of the line of sight. We know the orientation of these
objects with great certainty. The large BEL FWHM, , in ULQSOs tend to indicate that the BEL gas has a larger
component of axial velocity (either random or in a wind) along the jet
direction than previously thought.Comment: To appear in ApJ Letter
Note on the Electron Energy Spectrum in the Inner Van Allen Belt
Electron energy spectrum in the inner van allen bel
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