Can the cosmological constant undergo abrupt changes?

The existence of a simple spherically symmetric and static solution of the Einstein equations in the presence of a cosmological constant vanishing outside a definite value of the radial distance is investigated. A particular succession of field configurations, which are solutions of the Einstein equations in the presence of the considered cosmological term and auxiliary external sources, is constructed. Then, it is shown that the associated succession of external sources tend to zero in the sense of the generalized functions. The type of weak solution that is found becomes the deSitter homogeneous space-time for the interior region, and the Schwartzschild space in the outside zone.Comment: 10 pages, 1 figur

A domain-decomposition method to implement electrostatic free boundary conditions in the radial direction for electric discharges

At high pressure electric discharges typically grow as thin, elongated filaments. In a numerical simulation this large aspect ratio should ideally translate into a narrow, cylindrical computational domain that envelops the discharge as closely as possible. However, the development of the discharge is driven by electrostatic interactions and, if the computational domain is not wide enough, the boundary conditions imposed to the electrostatic potential on the external boundary have a strong effect on the discharge. Most numerical codes for electric discharges circumvent this problem by either using a wide computational domain or by calculating the boundary conditions by integrating the Green's function of an infinite domain. Here we describe an accurate and efficient method to impose free boundary conditions for an elongated electric discharge. To facilitate the use of our method we provide a sample implementation.Comment: 21 pages, 4 figures, a movie and a sample code in python. A new Appendix has been adde

Long-lived Colored Scalars at the LHC

We study the collider signatures of a long-lived massive colored scalar transforming trivially under the weak interaction and decaying within the inner sections of a detector such as ATLAS or CMS. In our study, we assume that the colored scalar couples at tree-level to a top quark and a stable fermion, possibly arising from a dark sector or from supersymmetric extensions of the Standard Model. After implementing the latest experimental searches for long-lived colored scalars, we observe a region of parameter space consistent with a colored electroweak-singlet scalar with mass between $\sim200-350$ GeV and a lifetime between $0.1-1$ $\text{mm}/c$ together, with a nearly degenerate dark fermion that may be probed at the $\sqrt{s}=13$ TeV LHC. We show that a search strategy using a combination of cuts on missing transverse energy and impact parameters can exclude regions of parameter space not accessed by prompt searches. We show that a region of parameter space within our simplified model may naturally arise from the light-stop window regime of supersymmetric extensions of the Standard Model, where a light mostly right-handed stop has a mass slightly larger than the lightest neutralino and decays through a four-body process

Statistical and entanglement entropy for black holes in quantum geometry

We analyze the relationship between entanglement (or geometric) entropy with statistical mechanical entropy of horizon degrees of freedom when described in the framework of isolated horizons in loop quantum gravity. We show that, once the relevant degrees of freedom are identified, the two notions coincide. The key ingredient linking the two notions is the structure of quantum geometry at Planck scale implied by loop quantum gravity, where correlations between the inside and outside of the black hole are mediated by eigenstates of the horizon area operator.Comment: References adde

Martingales and arbitrage: a new look

This paper addresses the equivalence between the absence of arbitrage and the existence of equivalent martingale measures. The equivalence will be established under quite weak assumptions since there are no conditions on the set of trading dates (it may be finite or infinite, with bounded or unbounded horizon, etc.) or on the trajectories of the price process (for instance, they do not have to be right-continuous). Besides we will deal with arbitrage portfolios rather than free-lunches. The concept of arbitrage is much more intuitive than the concept of free lunch and has more clear economic interpretation. Furthermore it is more easily tested in theoretical models or practical applications. In order to overcome the usual mathematical difficulties arising when dealing with arbirage strategies, the set of states of nature will be widened by drawing on projective systems of Radon probability measures, whose projective limit will be the martingale measure. The existence of densities between the "real" probabilities and the "risk-neutral" probabilities will be guaranteed by introducing the concept of "projective equivalence". Hence some classical counter-examples will be solved and a complete characterization of the absence of arbitrage will be provided in a very general framework

Winners and Losers of the Greek Crisis as a Result of a Double Fragmentation and Exclusion: A Discourse Analysis of Greek Civil Society

This article aims to explore, through the civil society’s opinion, the polarisation between ‘winners’ and ‘losers’ and the group of the ‘new excluded’, or ‘new poor’, that has emerged as a result of the European economic crisis and the social transformations that followed in the Greek society. Based on the Theory of Justice introduced by John Rawls (1971), and using the approach of Critical Discourse Analysis, this study focuses on the discourse analysis of the perception of 97 representatives of local and national NGOs, both formal and informal. The main results focus on different self and others’ presentations, especially during the economic crisis, and on the creation of an unbalanced, fragmented and exclusion-cantered society. However, the definition of rich and poor appears ambiguous through the analysis of various linguistic strategies of Greek NGOs revealing a hidden face of the societ

Anemia and Child Education: The Case of Colombia

Welfare programs in Colombia have been focused on reducing malnutrition and hunger and on increasing school attendance rates. However, there is not much evidence on the hypothesized relationship between nutrition and education. Using the National Survey of Nutritional Status in Colombia - 2005 (ENSIN) and the Demographic and Health Survey -2005 (DHS), this paper estimates the impact of nutrition on schooling outcomes. The results suggest that anemic children have a higher probability of lagging behind in school. Malnutrition, defined by anthropometric measures, does not have an impact on schooling lags. School attendance seems to be unrelated to nutrition measures. The results are consistent under different specifications.school attendance, schooling lag, nutrition, micronutrients