A family of relativistic charged thin disks with an inner edge

A new family of exact solutions of the Einstein-Maxwell equations for static axially symmetric spacetimes is presented. The metric functions of the solutions are explicitly computed and are simply written in terms of the oblate spheroidal coordinates. The solutions, obtained by applying the Ernst method of complex potentials, describe an infinite family of static charged dust disks with an inner edge. The energy density, pressure and charge density of all the disks of the family are everywhere well behaved, in such a way that the energy-momentum tensor fully agrees with all the energy conditions.   A new family of exact solutions of the Einstein-Maxwell equations for static axially symmetric spacetimes is presented. The metric functions of the solutions are explicitly computed and are simply written in terms of the oblate spheroidal coordinates. The solutions, obtained by applying the Ernst method of complex potentials, describe an infinite family of static charged dust disks with an inner edge. The energy density, pressure and charge density of all the disks of the family are everywhere well behaved, in such a way that the energy-momentum tensor fully agrees with all the energy conditions.  &nbsp

A family of relativistic charged thin disks with an inner edge

A new family of exact solutions of the Einstein-Maxwell equations for static axially symmetric spacetimes is presented. The metric functions of the solutions are explicitly computed and are simply written in terms of the oblate spheroidal coordinates. The solutions, obtained by applying the Ernst method of complex potentials, describe an infinite family of static charged dust disks with an inner edge. The energy density, pressure and charge density of all the disks of the family are everywhere well behaved, in such a way that the energy-momentum tensor fully agrees with all the energy conditions.   A new family of exact solutions of the Einstein-Maxwell equations for static axially symmetric spacetimes is presented. The metric functions of the solutions are explicitly computed and are simply written in terms of the oblate spheroidal coordinates. The solutions, obtained by applying the Ernst method of complex potentials, describe an infinite family of static charged dust disks with an inner edge. The energy density, pressure and charge density of all the disks of the family are everywhere well behaved, in such a way that the energy-momentum tensor fully agrees with all the energy conditions.  &nbsp

Relativistic static thin dust disks with an inner edge: An infinite family of new exact solutions

An infinite family of new exact solutions of the Einstein vacuum equations for static and axially symmetric spacetimes is presented. All the metric functions of the solutions are explicitly computed and the obtained expressions are simply written in terms of oblate spheroidal coordinates. Furthermore, the solutions are asymptotically flat and regular everywhere, as it is shown by computing all the curvature scalars. These solutions describe an infinite family of thin dust disks with a central inner edge, whose energy densities are everywhere positive and well behaved, in such a way that their energy-momentum tensor are in fully agreement with all the energy conditions. Now, although the disks are of infinite extension, all of them have finite mass. The superposition of the first member of this family with a Schwarzschild black hole was presented previously [G. A. Gonz\'alez and A. C. Guti\'errez-Pi\~neres, arXiv: 0811.3002v1 (2008)], whereas that in a subsequent paper a detailed analysis of the corresponding superposition for the full family will be presented.Comment: 9 pages, 3 figure

The struggle for existence in the world market ecosystem

The global trade system can be viewed as a dynamic ecosystem in which exporters struggle for resources: the markets in which they export. We can think that the aim of an exporter is to gain the entirety of a market share (say, car imports from the United States). This is similar to the objective of an organism in its attempt to monopolize a given subset of resources in an ecosystem. In this paper, we adopt a multilayer network approach to describe this struggle. We use longitudinal, multiplex data on trade relations, spanning several decades. We connect two countries with a directed link if the source country's appearance in a market correlates with the target country's disappearing, where a market is defined as a country-product combination in a given decade. Each market is a layer in the network. We show that, by analyzing the countries' network roles in each layer, we are able to classify them as out-competing, transitioning or displaced. This classification is a meaningful one: when testing the future export patterns of these countries, we show that out-competing countries have distinctly stronger growth rates than the other two classes

A family of relativistic charged thin disks with an inner edge

A new family of exact solutions of the Einstein-Maxwell equations for static axially symmetric spacetimes is presented. The metric functions of the solutions are explicitly computed and are simply written in terms of the oblate spheroidal coordinates. The solutions, obtained by applying the Ernst method of complex potentials, describe an infinite family of static charged dust disks with an inner edge. The energy density, pressure and charge density of all the disks of the family are everywhere well behaved, in such a way that the energy-momentum tensor fully agrees with all the energy conditions