Wiggly tails: a gravitational wave signature of massive fields around black holes

Massive fields can exist in long-lived configurations around black holes. We examine how the gravitational wave signal of a perturbed black hole is affected by such `dirtiness' within linear theory. As a concrete example, we consider the gravitational radiation emitted by the infall of a massive scalar field into a Schwarzschild black hole. Whereas part of the scalar field is absorbed/scattered by the black hole and triggers gravitational wave emission, another part lingers in long-lived quasi-bound states. Solving numerically the Teukolsky master equation for gravitational perturbations coupled to the massive Klein-Gordon equation, we find a characteristic gravitational wave signal, composed by a quasi-normal ringing followed by a late time tail. In contrast to `clean' black holes, however, the late time tail contains small amplitude wiggles with the frequency of the dominating quasi-bound state. Additionally, an observer dependent beating pattern may also be seen. These features were already observed in fully non-linear studies; our analysis shows they are present at linear level, and, since it reduces to a 1+1 dimensional numerical problem, allows for cleaner numerical data. Moreover, we discuss the power law of the tail and that it only becomes universal sufficiently far away from the `dirty' black hole. The wiggly tails, by constrast, are a generic feature that may be used as a smoking gun for the presence of massive fields around black holes, either as a linear cloud or as fully non-linear hair.Comment: 6 pages, 4 figure

Endohedrally confined hydrogen atom with a moving nucleus

We studied the hydrogen atom as a system of two quantum particles in different confinement conditions; a spherical-impenetrable-wall cavity and a fullerene molecule cage. The motion is referred to the center of spherical cavities, and the Schr\"{o}dinger equation solved by means of a Generalized Sturmian Function expansion in spherical coordinates. The solutions present different properties from the ones described by the many models in the literature, where the proton is fixed in space and only the electron is considered as a quantum particle. Our results show that the position of the proton (i.e. the center of mas of the H atom) is very sensitive to the confinement condition, and could vary substantially from one state to another, from being sharply centered to being localized outside the fullerene molecule. Interchange of the localization characteristics between the states when varying the strength of the fullerene cage and mass occurred through crossing phenomena

Nonparametric Tests for Conditional Symmetry in Dynamic Models

This article proposes omnibus tests for conditional symmetry around a parametric function in a dynamic context. Conditional moments may not exist or may depend on the explanatory variables. Test statistics are suitable functionals of the empirical process of residuals and explanatory variables, whose limiting distribution under the null is nonpivotal. The tests are implemented with the assistance of a bootstrap method, which is justified assuming very mild regularity conditions on the specification of the center of symmetry and the underlying serial dependence structure. Finite sample properties are examined by means of a Monte Carlo experiment.Publicad

Social Security Reform with Uninsurable Income Risk and Endogenous Borrowing Constraints

We study the aggregate effects of a social security reform in a large overlapping generations model where markets are incomplete and households face uninsurable idiosyncratic income shocks. We depart from the previous literature by assuming that, because of lack of commitment in the credit market, the borrowing constraint in the unique asset is endogenously determined by the agents' incentives to default on previous debts. We find that a model with exogenous borrowing constraints overestimates the positive effect of reforming social security on the capital stock and the saving rate, compared to our model with endogenous borrowing limit. The reason is that, in the latter, the size of precautionary savings is smaller because after the reform the incentives to default on previous debts are lower and consequently households face more relaxed borrowing limits. Adding retirement accounts to the basic model does not change these conclusions, although the quantitative importance of endogenizing borrowing constraints is reduced.

Análisis de la capacidad de soporte sísmica de fundaciones superficiales

Indexación: Web of Science; Scielo.In the context of engineering practice, the problem of the seismic bearing capacity of shallow foundations has been solved indirectly, either due an increase of the static allowable soil pressures related to the probability of occurrence of the design earthquake or by adopting an equivalent pseudo-static approach. However, during last decades, a series of analytical methods that directly address the problem from the seismic point of view has been developed. This paper presents a parametric comparative analysis of different methods for estimating seismic bearing capacity of shallow strip foundations. Analytical methods, developed in the framework of both limit equilibrium and limit analysis theories, and also simplified design procedures typically used in practice were considered. The results obtained show an important decrease of the bearing foundation capacity with increasing of the maximum earthquake acceleration, which highlights the need to obtain a measure of the reliability associated with both calculation methods and safety factors commonly used for seismic design.En el contexto de la práctica ingenieril, el problema de la capacidad de soporte sísmica de fundaciones superficiales generalmente ha sido resuelto, de modo indirecto, ya sea considerando un incremento en las tensiones admisibles estáticas del suelo, asociado a la probabilidad de ocurrencia de un cierto evento sísmico de diseño, o bien adoptando un enfoque de tipo pseudoestático equivalente. Sin embargo, durante las últimas décadas se han desarrollado una serie de métodos analíticos que abordan directamente el problema desde el punto de vista sísmico. Este artículo presenta un análisis comparativo de tipo paramétrico entre diferentes métodos para estimar la capacidad de soporte sísmica de fundaciones superficiales corridas. Se consideraron métodos analíticos, desarrollados en el contexto de las teorías de equilibrio límite y análisis límite, y también procedimientos de diseño simplificados típicamente utilizados en la práctica. Los resultados obtenidos muestran un importante deterioro de la capacidad de soporte de la fundación en la medida que la aceleración máxima del sismo aumenta, lo cual pone de manifiesto la necesidad de establecer una medida de la confiabilidad asociada a los métodos de cálculo y factores de seguridad comúnmente usados para diseño sísmico.http://ref.scielo.org/kp4j8