Gravitational Wave Emission and Mass Extraction from a Perturbed Schwarzschild Black Hole (continue)

A relativistic model for the emission of gravitational waves from an initially unperturbed Schwarzschild black hole, or spherical collapsing configuration, is completely integrated. The model consists basically of gravitational perturbations of the Robinson-Trautman type on the Schwarzschild spacetime. In our scheme of perturbation, gravitational waves may extract mass from the collapsing configuration. Robinson-Trautmann perturbations also include another mode of emission of mass, which we denote shell emission mode: in the equatorial plane of the configuration, a timelike $(1+2)$ shell of matter may be present, whose stress-energy tensor is modelled by neutrinos and strings emitted radially on the shell; no gravitational waves are present in this mode. The invariant characterization of gravitational wave perturbations and of the gravitational wave zone is made through the analysis of the structure of the curvature tensor and the use of the Peeling Theorem.Comment: 26 pages, LaTex, no figure

Gravitational wave recoils in non-axisymmetric Robinson-Trautman spacetimes

We examine the gravitational wave recoil waves and the associated net kick velocities in non-axisymmetric Robinson-Trautman spacetimes. We use characteristic initial data for the dynamics corresponding to non-head-on collisions of black holes. We make a parameter study of the kick distributions, corresponding to an extended range of the incidence angle $\rho_0$ in the initial data. For the range of $\rho_0$ examined ($3^{\circ} \leq \rho_0 \leq 110^{\circ}$) the kick distributions as a function of the symmetric mass parameter $\eta$ satisfy a law obtained from an empirical modification of the Fitchett law, with a parameter $C$ that accounts for the non-zero net gravitational momentum wave fluxes for the equal mass case. The law fits accurately the kick distributions for the range of $\rho_0$ examined, with a rms normalized error of the order of $5 \%$. For the equal mass case the nonzero net gravitational wave momentum flux increases as $\rho_0$ increases, up to $\rho_0 \simeq 55^{\circ}$ beyond which it decreases. The maximum net kick velocity is about $190 {\rm km/s}$ for for the boost parameter considered. For $\rho_0 \geq 50^{\circ}$ the distribution is a monotonous function of $\eta$. The angular patterns of the gravitational waves emitted are examined. Our analysis includes the two polarization modes present in wave zone curvature.Comment: 10 pages, 5 figures. arXiv admin note: substantial text overlap with arXiv:1403.4581, arXiv:1202.1271, arXiv:1111.122

Simulation of subcritical crack propagation in quase-brittle materials applying a version of the discrete element method formed by beams

Há numerosas aplicações de interesse tecnológico onde materiais de comportamento quase frágil, como é o caso de materiais cimentícios, rochas e materiais compostos formados pela mistura de cerâmicas com outras fases, são submetidos a cargas oscilantes e sofrem degradação das suas propriedades. Desenvolver ferramentas de análise que permitam entender e prever os mecanismos que governam esta degradação é um problema aberto na engenharia moderna. Neste contexto, no presente trabalho, se utiliza uma versão do método dos elementos discretos (DEM) formado por barras para explorar as possibilidades do mesmo na simulação dos mecanismos de degradação que ocorrem em materiais quase frágeis quando submetidos à fadiga. Simulações sobre corpos de prova de geometria simples são apresentadas e vários aspectos deste problema são discutidos, entre eles: é explorada a relação entre os parâmetros micro e macromecânicos do modelo empregado e como o efeito de escala é capturado e influi nesta relação. Os resultados preliminares apresentados deixam em evidência a potencialidade da metodologia proposta para compreender os micromecanismos de dano que ocorrem nos materiais quase frágeis e também para predizer sua evolução.There are numerous applications, of technological interest, where materials of quasi‐brittle behavior, as in the case of cement‐based composite materials, rocks and composites formed by the mixture of ceramics with other phases, are subjected to oscillating loads and suffer degradation of its properties. To develop analysis tools that allow to understand and to predict this degradation governing mechanisms is an opened problem in modern engineering. In this context, in the present work, it is used a version of the discrete element method formed by beams to explore its possibilities in simulating the degradation mechanisms that occur in quasi‐brittle materials when subjected to fatigue. Simulations over simple geometry test subjects are presented and several aspects of this problem are discussed and among the problems: it is explored the relationship between micro and macro mechanic parameters of the used model and how the scale effect is captured and influences this relationship. The presented preliminary results show the potentiality of the proposed methodology to understand the micro mechanisms of damage that occur in quasi‐brittle materials and also to predict its evolution.Peer Reviewe