6,302 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 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
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
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 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
Aligned electric and magnetic Weyl fields
We analyze the spacetimes admitting a direction for which the relative
electric and magnetic Weyl fields are aligned. We give an invariant
characterization of these metrics and study the properties of its Debever null
vectors. The directions 'observing' aligned electric and magnetic Weyl fields
are obtained for every Petrov type. The results on the no existence of purely
magnetic solutions are extended to the wider class having homothetic electric
and magnetic Weyl fields.Comment: 14 page
Positioning systems in Minkowski space-time: from emission to inertial coordinates
The coordinate transformation between emission coordinates and inertial
coordinates in Minkowski space-time is obtained for arbitrary configurations of
the emitters. It appears that a positioning system always generates two
different coordinate domains, namely, the front and the back emission
coordinate domains. For both domains, the corresponding covariant expression of
the transformation is explicitly given in terms of the emitter world-lines.
This task requires the notion of orientation of an emitter configuration. The
orientation is shown to be computable from the emission coordinates for the
users of a `central' region of the front emission coordinate domain. Other
space-time regions associated with the emission coordinates are also outlined.Comment: 20 pages; 1 figur
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