Competitive issue of money & abolition of central banks

The aim of this work is to analyze the main characteristics of the current financial system and to investigate the arising of critical voices with respect this system. In particular, we analyze some historical facts that have been important in the creation of this financial order. We analyze the new digital currency, known as Bitcoin, as the basic ingredient in the formation of a new alternative and decentralized international financial system. In 10 years Bitcoin has expanded its influence to many economic activities. We also analyzed briefly the classic liberal theory that criticizes the intervention of governments in the markets. Finally, we consider relevant the arising of a group of countries (BRICS) that may challenge the current system where the position of USA is privileged.

Hartle's model within the general theory of perturbatiye matchings: the change in mass

Hartle's model provides the most widely used analytic framework to describe isolated compact bodies rotating slowly in equilibrium up to second order in perturbations in the context of General Relativity. Apart from some explicit assumptions, there are some implicit, like the "continuity" of the functions in the perturbed metric across the surface of the body. In this work we sketch the basics for the analysis of the second order problem using the modern theory of perturbed matchings. In particular, the result we present is that when the energy density of the fluid in the static configuration does not vanish at the boundary, one of the functions of the second order perturbation in the setting of the original work by Hartle is not continuous. This discrepancy affects the calculation of the change in mass of the rotating star with respect to the static configuration needed to keep the central energy density unchanged.