17,821 research outputs found
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
An intrinsic characterization of 2+2 warped spacetimes
We give several equivalent conditions that characterize the 2+2 warped
spacetimes: imposing the existence of a Killing-Yano tensor subject to
complementary algebraic restrictions; in terms of the projector (or of the
canonical 2-form ) associated with the 2-planes of the warped product. These
planes are principal planes of the Weyl and/or Ricci tensors and can be
explicitly obtained from them. Therefore, we obtain the necessary and
sufficient (local) conditions for a metric tensor to be a 2+2 warped product.
These conditions exclusively involve explicit concomitants of the Riemann
tensor. We present a similar analysis for the conformally 2+2 product
spacetimes and give an invariant classification of them. The warped products
correspond to two of these invariant classes. The more degenerate class is the
set of product metrics which are also studied from an invariant point of view.Comment: 18 pages; submitted to Class. Quantum Grav
Coll Positioning systems: a two-dimensional approach
The basic elements of Coll positioning systems (n clocks broadcasting
electromagnetic signals in a n-dimensional space-time) are presented in the
two-dimensional case. This simplified approach allows us to explain and to
analyze the properties and interest of these relativistic positioning systems.
The positioning system defined in flat metric by two geodesic clocks is
analyzed. The interest of the Coll systems in gravimetry is pointed out.Comment: 6 pages; in Proc. Spanish Relativity Meeting ERE-2005, Oviedo (Spain
Angular Pseudomomentum Theory for the Generalized Nonlinear Schr\"{o}dinger Equation in Discrete Rotational Symmetry Media
We develop a complete mathematical theory for the symmetrical solutions of
the generalized nonlinear Schr\"odinger equation based on the new concept of
angular pseudomomentum. We consider the symmetric solitons of a generalized
nonlinear Schr\"odinger equation with a nonlinearity depending on the modulus
of the field. We provide a rigorous proof of a set of mathematical results
justifying that these solitons can be classified according to the irreducible
representations of a discrete group. Then we extend this theory to
non-stationary solutions and study the relationship between angular momentum
and pseudomomentum. We illustrate these theoretical results with numerical
examples. Finally, we explore the possibilities of the generalization of the
previous framework to the quantum limit.Comment: 18 pages; submitted to Physica
Two Dimensional Quantum Chromodynamics as the Limit of Higher Dimensional Theories
We define pure gauge on an infinite strip of width . Techniques
similar to those used in finite allow us to relate -observables to
pure behaviors. The non triviality of the L \arrow 0 limit is proven
and the generalization to four dimensions described. The glueball spectrum of
the theory in the small width limit is calculated and compared to that of the
two dimensional theory.Comment: 12 pages written in LaTeX, figure available from the authors,
preprint Univ. of Valencia, FTUV/94-4
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