539 research outputs found
Computability of the causal boundary by using isocausality
Recently, a new viewpoint on the classical c-boundary in Mathematical
Relativity has been developed, the relations of this boundary with the
conformal one and other classical boundaries have been analyzed, and its
computation in some classes of spacetimes, as the standard stationary ones, has
been carried out.
In the present paper, we consider the notion of isocausality given by
Garc\'ia-Parrado and Senovilla, and introduce a framework to carry out
isocausal comparisons with standard stationary spacetimes. As a consequence,
the qualitative behavior of the c-boundary (at the three levels: point set,
chronology and topology) of a wide class of spacetimes, is obtained.Comment: 44 pages, 5 Figures, latex. Version with minor changes and the
inclusion of Figure
Isocausal spacetimes may have different causal boundaries
We construct an example which shows that two isocausal spacetimes, in the
sense introduced by Garc\'ia-Parrado and Senovilla, may have c-boundaries which
are not equal (more precisely, not equivalent, as no bijection between the
completions can preserve all the binary relations induced by causality). This
example also suggests that isocausality can be useful for the understanding and
computation of the c-boundary.Comment: Minor modifications, including the title, which matches now with the
published version. 12 pages, 3 figure
Causal symmetries
Based on the recent work \cite{PII} we put forward a new type of
transformation for Lorentzian manifolds characterized by mapping every causal
future-directed vector onto a causal future-directed vector. The set of all
such transformations, which we call causal symmetries, has the structure of a
submonoid which contains as its maximal subgroup the set of conformal
transformations. We find the necessary and sufficient conditions for a vector
field \xiv to be the infinitesimal generator of a one-parameter submonoid of
pure causal symmetries. We speculate about possible applications to gravitation
theory by means of some relevant examples.Comment: LaTeX2e file with CQG templates. 8 pages and no figures. Submitted to
Classical and Quantum gravit
On the causal properties of warped product spacetimes
It is shown that the warped product spacetime P=M *_f H, where H is a
complete Riemannian manifold, and the original spacetime M share necessarily
the same causality properties, the only exceptions being the properties of
causal continuity and causal simplicity which present some subtleties. For
instance, it is shown that if diamH=+\infty, the direct product spacetime P=M*H
is causally simple if and only if (M,g) is causally simple, the Lorentzian
distance on M is continuous and any two causally related events at finite
distance are connected by a maximizing geodesic. Similar conditions are found
for the causal continuity property. Some new results concerning the behavior of
the Lorentzian distance on distinguishing, causally continuous, and causally
simple spacetimes are obtained. Finally, a formula which gives the Lorentzian
distance on the direct product in terms of the distances on the two factors
(M,g) and (H,h) is obtained.Comment: 22 pages, 2 figures, uses the package psfra
A new special class of Petrov type D vacuum space-times in dimension five
Using extensions of the Newman-Penrose and Geroch-Held-Penrose formalisms to
five dimensions, we invariantly classify all Petrov type vacuum solutions
for which the Riemann tensor is isotropic in a plane orthogonal to a pair of
Weyl alligned null directionsComment: 4 pages, 1 table, no figures. Contribution to the proceedings of the
Spanish Relativity Meeting 2010 held in Granada (Spain
A Note on Non-compact Cauchy surface
It is shown that if a space-time has non-compact Cauchy surface, then its
topological, differentiable, and causal structure are completely determined by
a class of compact subsets of its Cauchy surface. Since causal structure
determines its topological, differentiable, and conformal structure of
space-time, this gives a natural way to encode the corresponding structures
into its Cauchy surface
Acute effects of exercise on mood and HRV
El objetivo del estudio es analizar los efectos agudos del ejercicio físico sobre el estado de ánimo y la variabilidad de la frecuencia cardíaca (HRV), en personas activas y sedentarias. Para ello participaron 30 estudiantes clasificados en Activos y No activos. En una sola sesión realizaban una prueba de esfuerzo submáximo (UKK), cumplimentando el Perfil de Estados de Ánimo (POMS) y realizando un test en reposo de la HRV antes y después del ejercicio. Los resultados indican una mejora en el estado de ánimo, aumentando en los factores de Vigor y Fatiga y disminuyendo en Tensión y Depresión después del ejercicio. Se encontraron diferencias significativas en función del nivel de ejercicio físico de los participantes en el nivel de Depresión, al observarse una mayor disminución después del ejercicio en los Activos. La HRV también mostró diferencias entre Activos y No activos en los parámetros de dominio frecuencial, LFnu2 y HFnu2The aim of this study was to analyze the acute effects of exercise on mood and on heart rate variability (HRV), in active and sedentary people. This involved 30 undergraduates classified into Active and Non active participants. In a single session participants performed a submaximal exercise test (UKK), answered the Profile of Mood States (POMS) and performed before and after the exercise a test of HRV at rest. The participants improved their mood state, by increasing Vigor and Fatigue factors and decreased Tension and Depression after the exercise test. Moreover, Active participants presented a significant higher decrease in Depression after exercise than Non active. HRV analysis also showed differences between Active and Non active participants in the frequency domain parameters LFnu2 and HFnu
Grain-size trends associated with sediment transport patterns in Cadiz Bay (southwest Iberian Peninsula)
En la zona infralitoral y de plataforma interna, las tendencias en los parámetros granulométricos permiten caracterizar ambientes antiguos y modernos, e identificar trayectorias de transporte de sedimentos mediante el análisis de las distribuciones granulométricas y el análisis factorial multivariante. En la bahía de Cádiz, las tendencias observadas en los parámetros granulométricos están controladas por los aportes de sedimentos finos, la configuración de la costa y las trayectorias de transporte en suspensión debidas a las corrientes de reflujo mareal. La asimetría es el parámetro principal en la identificación de tendencias granulométricas. Se han determinado tres tendencias que caracterizan los ambientes sedimentarios presentes: a) asimetrías muy positivas y distribuciones muy leptocúrticas indican un alto grado de madurez textural y retrabajamiento; b) tendencias hacia asimetrías negativas caracterizan ambientes intermareales de playa y permiten localizar ambientes paleolitorales; c) distribuciones simétricas y mal seleccionadas trazan las trayectorias permanentes de precipitación de sedimentos finos, mientras asimetrías más positivas, aumento del tamaño de grano y mejor selección marcan la extensión ocasional de las plumas de materia en suspensión.On the inner continental shelf and coastal environments, grain-size trends make it possible to characterise ancient and modern environments, and to identify net sediment transport patterns, using grain-size distributions and factorial multivariate analysis. In Cadiz Bay, grain-size trends are controlled by the contribution of fine sediments, coastal morphology and the suspended transport pathways due to the ebb-currents. The main parameter able to identify grain-size trends is skewness. Three trends were determined to characterise present-day sedimentary environments: a) very positively skewed sediments with leptokurtic distributions belong to deposits with a high degree of textural maturity and reworking; b) negatively skewed sediments characterise intertidal environments (foreshore), and also make it possible to localise palaeolittoral environments; c) symmetrical and poorly sorted distributions indicate the permanent fine-settling pathways, whereas positively skewed, coarser and better-sorted sediments point to the occasional extension of suspended matter plumes.Instituto Español de Oceanografí
Initial data sets for the Schwarzschild spacetime
A characterisation of initial data sets for the Schwarzschild spacetime is
provided. This characterisation is obtained by performing a 3+1 decomposition
of a certain invariant characterisation of the Schwarzschild spacetime given in
terms of concomitants of the Weyl tensor. This procedure renders a set of
necessary conditions --which can be written in terms of the electric and
magnetic parts of the Weyl tensor and their concomitants-- for an initial data
set to be a Schwarzschild initial data set. Our approach also provides a
formula for a static Killing initial data set candidate --a KID candidate.
Sufficient conditions for an initial data set to be a Schwarzschild initial
data set are obtained by supplementing the necessary conditions with the
requirement that the initial data set possesses a stationary Killing initial
data set of the form given by our KID candidate. Thus, we obtain an algorithmic
procedure of checking whether a given initial data set is Schwarzschildean or
not.Comment: 16 page
Further properties of causal relationship: causal structure stability, new criteria for isocausality and counterexamples
Recently ({\em Class. Quant. Grav.} {\bf 20} 625-664) the concept of {\em
causal mapping} between spacetimes --essentially equivalent in this context to
the {\em chronological map} one in abstract chronological spaces--, and the
related notion of {\em causal structure}, have been introduced as new tools to
study causality in Lorentzian geometry. In the present paper, these tools are
further developed in several directions such as: (i) causal mappings --and,
thus, abstract chronological ones-- do not preserve two levels of the standard
hierarchy of causality conditions (however, they preserve the remaining levels
as shown in the above reference), (ii) even though global hyperbolicity is a
stable property (in the set of all time-oriented Lorentzian metrics on a fixed
manifold), the causal structure of a globally hyperbolic spacetime can be
unstable against perturbations; in fact, we show that the causal structures of
Minkowski and Einstein static spacetimes remain stable, whereas that of de
Sitter becomes unstable, (iii) general criteria allow us to discriminate
different causal structures in some general spacetimes (e.g. globally
hyperbolic, stationary standard); in particular, there are infinitely many
different globally hyperbolic causal structures (and thus, different conformal
ones) on , (iv) plane waves with the same number of positive eigenvalues
in the frequency matrix share the same causal structure and, thus, they have
equal causal extensions and causal boundaries.Comment: 33 pages, 9 figures, final version (the paper title has been
changed). To appear in Classical and Quantum Gravit
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