Relativistic Positioning Systems: The Emission Coordinates

This paper introduces some general properties of the gravitational metric and the natural basis of vectors and covectors in 4-dimensional emission coordinates. Emission coordinates are a class of space-time coordinates defined and generated by 4 emitters (satellites) broadcasting their proper time by means of electromagnetic signals. They are a constitutive ingredient of the simplest conceivable relativistic positioning systems. Their study is aimed to develop a theory of these positioning systems, based on the framework and concepts of general relativity, as opposed to introducing `relativistic effects' in a classical framework. In particular, we characterize the causal character of the coordinate vectors, covectors and 2-planes, which are of an unusual type. We obtain the inequality conditions for the contravariant metric to be Lorentzian, and the non-trivial and unexpected identities satisfied by the angles formed by each pair of natural vectors. We also prove that the metric can be naturally split in such a way that there appear 2 parameters (scalar functions) dependent exclusively on the trajectory of the emitters, hence independent of the time broadcast, and 4 parameters, one for each emitter, scaling linearly with the time broadcast by the corresponding satellite, hence independent of the others.Comment: 13 pages, 3 figures. Only format changed for a new submission. Submitted to Class. Quantum Gra

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

Positioning systems in Minkowski space-time: Bifurcation problem and observational data

In the framework of relativistic positioning systems in Minkowski space-time, the determination of the inertial coordinates of a user involves the {\em bifurcation problem} (which is the indeterminate location of a pair of different events receiving the same emission coordinates). To solve it, in addition to the user emission coordinates and the emitter positions in inertial coordinates, it may happen that the user needs to know {\em independently} the orientation of its emission coordinates. Assuming that the user may observe the relative positions of the four emitters on its celestial sphere, an observational rule to determine this orientation is presented. The bifurcation problem is thus solved by applying this observational rule, and consequently, {\em all} of the parameters in the general expression of the coordinate transformation from emission coordinates to inertial ones may be computed from the data received by the user of the relativistic positioning system.Comment: 10 pages, 7 figures. The version published in PRD contains a misprint in the caption of Figure 3, which is here amende

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

A physical application of Kerr-Schild groups

The present work deals with the search of useful physical applications of some generalized groups of metric transformations. We put forward different proposals and focus our attention on the implementation of one of them. Particularly, the results show how one can control very efficiently the kind of spacetimes related by a Generalized Kerr-Schild (GKS) Ansatz through Kerr-Schild groups. Finally a preliminar study regarding other generalized groups of metric transformations is undertaken which is aimed at giving some hints in new Ans\"atze to finding useful solutions to Einstein's equations.Comment: 18 page

The self-coronation of Peter the Ceremonious (1336): historical, liturgical, and iconographical representations

Everything was ready for the solemn rite of the anointing and crowning of Peter IV of Aragon (1336–87). The ceremony was set for 14 April 1336 in Zaragoza's San Salvador Cathedral. The celebrant was to be the archbishop of Zaragoza, Pedro López de Luna y Ximénez de Urrea (1318–45), to whom the honor fell as metropolitan of the kingdom's capital. However, that spring morning there was a heated discussion in the vestry shortly before the start of proceedings. The king and the archbishop could not agree on who should place the crown on the new monarch's head. As a result the liturgy was delayed, to the consternation of the assembled throng packing Zaragoza Cathedral

Neutrino physics at accelerators

Present and future neutrino experiments at accelerators are mainly concerned with understanding the neutrino oscillation phenomenon and its implications. Here a brief account of neutrino oscillations is given together with a description of the supporting data. Some current and planned accelerator neutrino experiments are also explained.Comment: 23 pages, 24 figures. Talk given at the Corfu Summer Institute on Elementary Particle Physics 200

Nuevos datos magnetoestratigráficos del tránsito Oligoceno-Mioceno en el sector SE de la Cuenca del Ebro (provincia de Lleida, Zaragoza y Huesca, NE de España)

The study of two late Oligocene-early Miocene stratigraphic sections of alluvial and shallow lacustrine facies in the SE Ebro Basin has enabled the establishment of a high-resolution magnetostratigraphy for the Oligocene-Miocene boundary. The studied samples include alluvial sandstones and mudstones as well as shallow lacustrine limestones. A total of 121 stratigraphic levels, with an average sample spacing of -2.5 m, were sampled in two sections, using a portable gasoline powered dril1 machine. Core samples were cut in the laboratory into two or three standard specimens of 2.54 cm diameter X 2.1 cm in length. A minimum of two specimens per site were thermally or AF demagnetized in 8-9 steps at intervals of 50°C or 30°C, and intervals of 2.5 mT and 5 mT, respectively. The magnetic polarity zonation of the sections have been correlated to the Geomagnetic Polarity Time Scale (GPTS) allowing the recognition of Chrons 9r, 9n, 8r and 8n in the Mina Pilar section, and Chrons 6Cr, 6Cn, 6Br, 6Bn and 6AAr in the Valcuerna section. On the basis of magnetostratigraphic correlation it is deduced an interval of sedimentation time of -1.6 Ma for the Mina Pilar section, and 1.7-1.9 Ma for the Valcuerna section

Identifying and prioritizing demersal fisheries restricted areas based on combined ecological and fisheries criteria: The western Mediterranean

The western Mediterranean basin is a high marine biodiversity area under severe pressure by changing climate and intense human activities. Beyond national jurisdictions, international institutions such as the General Fisheries Commission for the Mediterranean (GFCM) work towards canalizing a regional consensus that fishing practices should evolve to better support the 2030 Agenda for Sustainable Development. In this context, Fisheries Restricted Areas (FRA) are proposed as effective management measures to contribute towards increasing fisheries sustainability in the region that can be considered, under some conditions, as Nature-based Solutions (NbS); however, how to operationalize their framework remains unclear. In this study, based on combined ecological and fisheries criteria, we identify and prioritize six potential priority areas for management (PAMs) in the western Mediterranean Sea. They are specifically aimed at the protection and recovery of Essential Fish Habitats and the conservation of Vulnerable Marine Ecosystems, whilst requiring limited adaptation of fisheries practices due to their relative low fishing pressure. We compare the identified areas to those that are currently under protection, and to areas that have been proposed for protection at the GFCM. Our results show that the FRAs and other spatial management measures introduced in the last years marginally contribute to the protection PAMs in the western Mediterranean region. However, the adoption of FRAs that are currently under discussion at the GFCM could contribute significantly to improve the situation. FRAs could also contribute to operationalize NbS in the western Mediterranean Sea when properly designed and implemented

Projected climate change impacts on upland heaths in Ireland

Heathland habitats in Ireland occur primarily in an oceanic setting which is strongly influenced by changes in the climate. As a consequence of the oceanic environment, Ireland has a high proportion of the northern Atlantic wet and alpine and boreal heaths of high conservation value within Europe. Future climate change is widely expected to place additional pressure on these systems. Seven bioclimatic envelope modelling techniques implemented in the BIOMOD modelling framework were used to model Wet and Alpine and Boreal heath distributions in Ireland. The 1961 to 1990 baseline models closely matched the observed distribution, and emphasise the strong dependency on climate. Mean winter precipitation, mean winter temperature and elevation were found to be important model components. The fitted models discrimination ability was assessed using the area under the curve (range 0.874 to 0.929, Wet heath; 0.858 to 0.936, Alpine and Boreal heath) of a receiver operating characteristic plot; the true skill statistic (range 0.648 to 0.713, Wet heath; 0.666 to 0.737, Alpine and Boreal heath); and Cohen’s kappa (range 0.652 to 0.714, Wet heath; 0.641 to 0.738, Alpine and Boreal heath). A BIOMOD ensemble prediction from all the models was used to project changes based on a climate change scenario for 2031 to 2060 dynamically downscaled from the Hadley Centre HadCM3-Q16 global climate model. The climate change projections for the individual models change markedly from the consistent baseline predictions. Projected climate space losses (gains) from the BIOMOD consensus model are -40.84% (limited expansion) and -10.38% (full expansion) for Wet heath; and -18.31% (limited expansion) and +28.17% (full expansion) for Alpine and Boreal heath. Although the consensus models project gains in climate space for both habitats in other parts of the country, new habitat formation in these areas is unlikely as current (and hence near future) land use and other conditions are not likely to favour expansion