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 $D$ 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

Causal Relationship: a new tool for the causal characterization of Lorentzian manifolds

We define and study a new kind of relation between two diffeomorphic Lorentzian manifolds called {\em causal relation}, which is any diffeomorphism characterized by mapping every causal vector of the first manifold onto a causal vector of the second. We perform a thorough study of the mathematical properties of causal relations and prove in particular that two given Lorentzian manifolds (say $V$ and $W$) may be causally related only in one direction (say from $V$ to $W$, but not from $W$ to $V$). This leads us to the concept of causally equivalent (or {\em isocausal} in short) Lorentzian manifolds as those mutually causally related. This concept is more general and of a more basic nature than the conformal relationship, because we prove the remarkable result that a conformal relation \f is characterized by the fact of being a causal relation of the {\em particular} kind in which both \f and \f^{-1} are causal relations. For isocausal Lorentzian manifolds there are one-to-one correspondences, which sometimes are non-trivial, between several classes of their respective future (and past) objects. A more important feature of isocausal Lorentzian manifolds is that they satisfy the same causality constraints. This indicates that the causal equivalence provides a possible characterization of the {\it basic causal structure}, in the sense of mutual causal compatibility, for Lorentzian manifolds. Thus, we introduce a partial order for the equivalence classes of isocausal Lorentzian manifolds providing a classification of spacetimes in terms of their causal properties, and a classification of all the causal structures that a given fixed manifold can have. A full abstract inside the paper.Comment: 47 pages, 10 figures. Version to appear in Classical and Quantum Gravit