7,251 research outputs found

### 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 $A$ subject to
complementary algebraic restrictions; in terms of the projector $v$ (or of the
canonical 2-form $U$) 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

### Vacuum type I spacetimes and aligned Papapetrou fields: symmetries

We analyze type I vacuum solutions admitting an isometry whose Killing
2--form is aligned with a principal bivector of the Weyl tensor, and we show
that these solutions belong to a family of type I metrics which admit a group
$G_3$ of isometries. We give a classification of this family and we study the
Bianchi type for each class. The classes compatible with an aligned Killing
2--form are also determined. The Szekeres-Brans theorem is extended to non
vacuum spacetimes with vanishing Cotton tensor.Comment: 19 pages; a reference adde

### On the classification of type D spacetimes

We give a classification of the type D spacetimes based on the invariant
differential properties of the Weyl principal structure. Our classification is
established using tensorial invariants of the Weyl tensor and, consequently,
besides its intrinsic nature, it is valid for the whole set of the type D
metrics and it applies on both, vacuum and non-vacuum solutions. We consider
the Cotton-zero type D metrics and we study the classes that are compatible
with this condition. The subfamily of spacetimes with constant argument of the
Weyl eigenvalue is analyzed in more detail by offering a canonical expression
for the metric tensor and by giving a generalization of some results about the
non-existence of purely magnetic solutions. The usefulness of these results is
illustrated in characterizing and classifying a family of Einstein-Maxwell
solutions. Our approach permits us to give intrinsic and explicit conditions
that label every metric, obtaining in this way an operational algorithm to
detect them. In particular a characterization of the Reissner-Nordstr\"{o}m
metric is accomplished.Comment: 29 pages, 0 figure

### On the separable quotient problem for Banach spaces

While the classic separable quotient problem remains open, we survey general
results related to this problem and examine the existence of a particular
infinitedimensional separable quotient in some Banach spaces of vector-valued
functions, linear operators and vector measures. Most of the results presented
are consequence of known facts, some of them relative to the presence of
complemented copies of the classic sequence spaces c_0 and l_p, for 1 <= p <=
\infty. Also recent results of Argyros - Dodos - Kanellopoulos, and Sliwa are
provided. This makes our presentation supplementary to a previous survey (1997)
due to Mujica

### 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 approach to relativistic positioning systems

A relativistic positioning system is a physical realization of a coordinate
system consisting in four clocks in arbitrary motion broadcasting their proper
times. The basic elements of the relativistic positioning systems are presented
in the two-dimensional case. This simplified approach allows to explain and to
analyze the properties and interest of these new systems. The positioning
system defined by geodesic emitters in flat metric is developed in detail. The
information that the data generated by a relativistic positioning system give
on the space-time metric interval is analyzed, and the interest of these
results in gravimetry is pointed out.Comment: 11 pages, 5 figures. v2: a brief description of the principal
bibliography has been adde

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