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We investigate the numerical stability of accelerating AdS black holes against linear scalar perturbations. In particular, we study the evolution of a probe non-minimally coupled scalar field on Schwarzschild and Reissner-Nordström AdS black holes with small accelerations by computing the quasinormal modes of the perturbation spectrum. We decompose the scalar field Klein-Gordon equation and study the eigenvalue problem for its angular and radial-temporal parts using different numerical methods. The angular part is written in terms of the Heun solution and expanded through the Frobenius method which turns out to give eigenvalues qualitatively similar to the ones obtained through the spherical harmonics representation. The radial-temporal evolution renders a stable field profile which is decomposed in terms of damped and purely imaginary oscillations of the quasinormal modes. We calculate the respective frequencies for different spacetime parameters showing the existence of a fine-structure in the modes, for both real and imaginary parts, which is not present in the non-accelerating AdS black holes. Our results indicate that the Schwarzschild and Reissner-Nordström AdS black holes with small accelerations are stable against linear scalar perturbations.

O artigo apresenta o projeto de extensao “Educacao Ambiental: conscientizacao para a construcao de futuros”, desenvolvido por professores e estudantes de Engenharia Ambiental e Sanitaria junto ao Programa Social “Viver Acoes Sociais”, no municipio de Chapeco, Santa Catarina. No texto, sao apresentados os processos e os produtos audiovisuais da interacao remota assincrona – imposta pela disseminacao e contaminacao da COVID-19 – com um grupo de criancas com idades entre 6 e 10 anos, no periodo de marco a agosto de 2020. O percurso metodologico – participativo e colaborativo – de definicao e construcao dos conteudos estruturou as discussoes em torno dos seguintes temas: (a) cuidados com o meio ambiente, (b) residuos solidos e reciclagem, (c) recurso natural agua, e (d) energias renovaveis. Apesar das dificuldades tecnologicas, os resultados demonstram importantes compreensoes acerca da conscientizacao ambiental, da ampliacao dos conhecimentos e do desenvolvimento de um pensamento critico acerca dos temas propostos.

Open Design (OD) is characterized as fast-growing community-based generative process, that is supported in a digital repository or platform, in order to develop a specific topic area or field. Many examples of OD are available nowadays, from software (probably the most common) to hardware, and from science and technology to business. One of the most known platforms of OD is an open editable content encyclopedia, the Wikipedia. Trough the involvement of volunteers (community that do not receive any payment for the work) in writing articles in a collaborative way was possible to develop, most probably, the extensive multi-language encyclopedia in the World started from scratch within 18 years. Based on analysis made from available Wikipedia statistical data, it is possible to conclude that from a stochastic behaviour the variables reached a transition phase in which a presence of a hysteresis between all variables were reached in between 60 to 80 months, and the editors (agents of the community) are an important asset for the system “transformation”.

Many of the developments started by social initiatives (bottom-up), others are induced by policies (top-down) or even by both (social and political). Open Design is mainly characterized as a movement generated by and for the community but could also be nourished by private/associative initiatives with the community support, and could be encourage by public entities that perceives Open Design as a flourish method for innovation and leading for a real democratization of the manufacturing. In this paper, three CAD software based on Open Design (rattleCAD, BRL CAD and FreeCAD) are evaluated, according to the number of downloads made in SourceFourge, in order to better understand the usage behavior of these CAD systems. The main findings suggest instability in the short range and stability in the medium and long range, indicating that the communities are active and providing attractive solutions.

O artigo apresenta o projeto de extensão “Educação Ambiental: conscientização para a construção de futuros” desenvolvido por professores e estudantes de Engenharia Ambiental e Sanitária junto ao Programa Social “Viver Ações Sociais” no município de Chapecó-SC. O Programa Viver é um espaço de educação não-formal de crianças e adolescentes em idade escolar entre 6 e 15 anos, nos diferentes aspectos que contemplam uma formação integral, cidadã e crítica. As atividades educativas no âmbito da educação ambiental foram desenvolvidas junto a turmas de crianças com idade entre 6 e 10 anos, levando uma transliteração dos eixos de formação do curso de Engenharia Ambiental e Sanitária da UFFS campus Chapecó – saneamento, recursos hídricos, energias renováveis e gestão ambiental. As oficinas tiveram caráter formativo com práticas diversas como brincadeiras, representações pictóricas, trabalhos em equipe de exploração e afins e tiveram como objetivo a promoção da conscientização ambiental, a ampliação dos conhecimentos e o desenvolvimento de um pensamento crítico acerca dos temas propostos. Durante o período de realização das atividades conseguimos uma satisfatória participação e envolvimento das crianças e através das atividades avaliativas percebemos que, de fato, conseguiram compreender o objetivo do projeto, fixar os principais conceitos trabalhados, e repensar ações – individuais e coletivas – na relação com o meio ambiente. Palavras-chave: Consciência ambiental; Oficinas socioambientais; Formação cidadã University extension in engineering: environmental education classes for socially vulnerable children Abstract: In this paper we present the communitarian project “Environmental Education” carried out by environmental engineering professors and students together with social local action of “Viver Ações Sociais” in Chapeco, Santa Catarina, Brazil. The social action of the “Programa Viver” performs non-formal learning with 6th to 15th aged students in multiple aspects within a perspective of critical and citizenship education. The activities performed by the organizers (students and professors) were carried out with children from 6 to 10 years old, considering the four different branches in the Environmental Engineering of UFFS campus Chapeco – sanitation, water resources, renewable energy and environmental management. The appointments were realized with different practices such as pictorial representations, work team aiming at environmental awareness, knowledge amplification and critical thinking on the proposed subjects. During the period of performance of the activities we achieved a satisfactory participation and involvement of the children, and through the evaluative activities we realized that, in fact, they understood the objective of the project, fixing the main concepts worked on, and rethinking actions - individual and collective - in relation to the environment. Keywords: environmental awareness; socio-environmental workshop; citizenship education

Black holes found in binaries move at very high velocities relative to our own reference frame and can accelerate due to the emission of gravitational radiation. Here, we investigate the numerical stability and late-time behavior of linear scalar perturbations in accelerating black holes described by the $C-$metric. We identify a family of quasinormal modes associated with the photon surface and a brand new family of purely imaginary modes associated with the boost parameter of the accelerating black hole spacetime. When the accelerating black hole is charged, we find a third family of modes which dominates the ringdown waveform near extremality. Our frequency and time domain analysis indicate that such spacetimes are stable under scalar fluctuations, while the late-time behavior follows an exponential decay law, dominated by quasinormal modes. This result is in contrast with the common belief that such perturbations, for black holes without a cosmological constant, always have a power-law cutoff. In this sense, our results suggest that the asymptotic structure of black hole backgrounds does not always dictate how radiative fields behave at late times., 15 pages, 8 figures, matches published version

We consider the equivalence of quasinormal modes and geodesic quantities recently brought back due to the black hole shadow observation by Event Horizon Telescope. Using WKB method we found an analytical relation between the real part of quasinormal frequencies at the eikonal limit and black hole shadow radius. We verify this correspondence with two black hole families in $4$ and $D$ dimensions, respectively., Comment: 13 pages, 1 figure

The strong cosmic censorship hypothesis has recently regained a lot of attention in charged and rotating black holes immersed in de Sitter space. Although the picture seems to be clearly leaning towards the validity of the hypothesis in Kerr-de Sitter geometries, Reissner-Nordstr\"{o}m-de Sitter black holes appear to be serious counter-examples. Here, we perform another test to the hypothesis by using a scalar field perturbation non-minimally coupled to the Einstein tensor propagating on Reissner-Nordstr\"{o}m-de Sitter spacetimes. Such non-minimal derivative coupling is characteristic of Horndeski scalar-tensor theories. Although the introduction of higher-order derivative couplings in the energy-momentum tensor increases the regularity requirements for the existence of weak solutions beyond the Cauchy horizon, we are still able to find a small finite region in the black hole's parameter space where strong cosmic censorship is violated., Comment: 21 pages, 5 figures, to appear in JHEP

We study the instability of a Reissner-Nordstr\"om-AdS (RNAdS) black hole under perturbations of a massive scalar field coupled to Einstein tensor. Calculating the potential of the scalar perturbations we find that as the strength of the coupling of the scalar to Einstein tensor is increasing, the potential develops a negative well outside the black hole horizon, indicating an instability of the background RNAdS. We then investigate the effect of this coupling on the quasinormal modes. We find that there exists a critical value of the coupling which triggers the instability of the RNAdS. We also find that as the charge of the RNAdS is increased towards its extremal value, the critical value of the derivative coupling is decreased., Comment: 18 pages, 6 figures

We determine the scalar field evolution of a braneworld localized black hole with both dark matter and dark energy components, obtained within a dynamical and continuous embedding formalism by use of Nash's theorem. We further extract the associated quasinormal modes for both de Sitter-Schwarzschild-Dark matter and anti-de Sitter-Schwarzschild-Dark matter solutions, for the different causal structures (one, two or three horizon spacetimes) given by the space of parameters. By comparison with standard General Relativity solutions, we infer possible observable astrophysical differences, and remark on modifications to previous AdS/CFT correspondence scenarios., 12 pages, 15 figures

Neste trabalho faremos uma investigação no campo das perturbações gravitacionais e propagação de ondas em geometrias de buracos negros com campos elétricos ou magnéticos. Usando uma geometria tipo Ernst-Melvin de um buraco negro massivo em um Universo com campo magnético no eixo z, calculamos os modos quasi-normais de propagação de um campo escalar, demonstrando que este se comporta como um campo escalar com massa 2|m|B em uma geometria de Schwarzschild, para pequenos valores do campo magnético B (correspondendo m ao número azimutal do esférico harmônico). Ainda com esta geometria, calculamos a contribuição de ondas escalares para a entropia do buraco negro em termos dos cut offs ultravioleta e infravermelho. Com uma solução do tipo Reissner-Nordström em 4 dimensões, investigamos as possíveis correspondências entre os modos quasinormais e as propriedades termodinâmicas deste buraco negro, atestando o resultado de que a conjectura Hod modificada por Maggiore é válida em tal solução. Também, com uma geometria de Reissner-Nordström-de Sitter D-dimensional, obtivemos os modos quasi-normais de vibração para dois potenciais diferentes, estabelecendo a ausência de modos instáveis para uma grande gama de parâmetros deste buraco negro. In this work we make an incursion into the branch of gravitational perturbations and field propagation around known-geometries of black holes with electromagnetic fields. Using an Ernst-Melvin type of geometry in a massive black hole immersed on a magnetic Universe, we calculate the quasi-normal modes of the propagating field, showing the equivalence of this problem with that of a massive scalar field (for which the mass is 2|m|B, m being the azhimutal number, and B the magnetic field) propagating around a Schwarzschild geometry. We also compute the contribution of the scalar field to the entropy of the black hole in terms of the infrared and ultraviolet cut offs. Using a Reissner-Nordstr¨om-like solution in 4 dimensions, we investigate the possible correspondence between quasi-normal modes and the thermodynamical properties of this black hole, atesting the validity of the modified Hod conjecture as proposed by Maggiore. Finally, for a Reissner-Nordstr¨om-de Sitter D-dimensional solution, we obtain the quasi-normal modes for two diferent potentials, establishing the absence of unstable modes for a large range of values for the black hole parameters.

Durante os últimos 90 anos temos visto o grande esplendor que a teoria da relatividade geral de Einstein alcançou em suas diversas previsões. Esta dissertação é um estudo a respeito desta teoria e suas extrapolações. Falaremos de início acerca da primeira solução das equações de Einstein para buracos negros obtida por Karl Schwarzschild em 1916: o buraco negro esfericamente simétrico e sem carga. Trataremos das possíveis órbitas neste tipo de solução bem como de perturbações gravitacionais e escalares. Ainda utilizando a solução de Schwarzschild, adentraremos os tópicos desenvolvidos recentemente em um tratamento semi-clássico da relatividade: a termodinâmica dos buracos negros. Posteriormente estudaremos as novas teorias com base na relatividade geral, que resolvem o problema da hierarquia buscando por dimensões extras em nosso Universo. Em tal contexto analisamos por exemplo como se comportam os buracos negros nestes Universos com mais do que 4 dimensões. Porém, estudamos perturbações gravitacionais em uma corda negra chegando a averiguar a presença de uma instabilidade para modos com comprimento de onda maiores do que o horizonte da corda (em uma aproximação linear), e demonstramos que em uma das possíveis soluções do problema da Hierarquia (Universos de Randall Sundrum) não existem atalhos gravitacionais mesmo para branas não planas (extrapolação dos Universos de Randall-Sundrum). Over the last 90 years Einstein`s Theory of General Relativity has had a tremendous success in all its predictions. This dissertation is concerned with the study of this theory and its extrapolations. We begin with the first solution of the Einstein equations for black holes obtained by Karl Schwarzschild at 1916: the spherically symmetric black hole without charge, obtaining the orbits and the scalar and gravitational perturbations around the metric. We also consider the recent developments in black hole thermodynamics via a semiclassical approach to the theory. Subsequently, we study the new theories based on general relativity extrapolations, which solve the hierarchy problem proposing extra dimensions in our Universe. In this context we analyze for example the behavior of black holes in Universes with more than 4 dimensions. Finally, we study the gravitational perturbations in a black string showing the presence of unstable modes with wave length bigger than the black string horizon. We also show that in one of the possible Universes which solve the hierarchy problem there are no gravitational shortcuts even for non-at branes (an extrapolation of Randall-Sundrum Universes).