Hyperboloidal approach for static spherically symmetric spacetimes: a didactical introduction and applications in black-hole physics

This work offers a didactical introduction to the calculations and geometrical properties of a static, spherically symmetric spacetime foliated by hyperboloidal time surfaces. We discuss the various degrees of freedom involved, namely the height function, responsible for introducing the hyperboloidal time coordinate, and a radial compactification function. A central outcome is the expression of the Trautman-Bondi mass in terms of the hyperboloidal metric functions. Moreover, we apply this formalism to a class of wave equations commonly used in black-hole perturbation theory. Additionally, we provide a comprehensive derivation of the hyperboloidal minimal gauge, introducing two alternative approaches within this conceptual framework: the in-out and out-in strategies. Specifically, we demonstrate that the height function in the in-out strategy follows from the well-known tortoise coordinate by changing the sign of the terms that become singular at future null infinity. Similarly, for the out-in strategy, a sign change also occurs in the tortoise coordinate's regular terms. We apply the methodology to the following spacetimes: Singularity-approaching slices in Schwarzschild, higher-dimensional black holes, black hole with matter halo, and Reissner- Nordstr\"om-de Sitter. From this heuristic study, we conjecture that the out-in strategy is best adapted for black hole geometries that account for environmental or effective quantum effects.Comment: 41 pages, 6 figures. Published to Philosophical Transactions A issue: "At the interface of asymptotics, conformal methods and analysis in general relativity" --- updated version to include referees suggestions and extend literatur

Holographic quenches and anomalous transport

We study the response of the chiral magnetic effect due to continuous quenches induced by time dependent electric fields within holography. Concretely, we consider a holographic model with dual chiral anomaly and compute the electric current parallel to a constant, homogeneous magnetic field and a time dependent electric field in the probe approximation. We explicitly solve the PDEs by means of pseudospectral methods in spatial and time directions and study the transition to an universal "fast" quench response. Moreover, we compute the amplitudes, i.e.,~residues of the quasi normal modes, by solving the (ODE) Laplace transformed equations. We investigate the possibility of considering the asymptotic growth rate of the amplitudes as a well defined notion of initial time scale for linearized systems. Finally, we highlight the existence of Landau level resonances in the electrical conductivity parallel to a magnetic field at finite frequency and show explicitly that these only appear in presence of the anomaly. We show that the existence of these resonances induces, among others, a long-lived AC electric current once the electric field is switched off.Comment: 34 pages, 10 figure

ESTRATÉGIAS ADOTADAS PELAS INSTITUIÇÕES DE ENSINO SUPERIOR DA REDE PRIVADA DE MINAS GERAIS FACE AS TRANSFORMAÇÕES NO INÍCIO DO SÉCULO XXI

As mudanças econômicas e políticas ocorridas a partir da segunda metade do século XX têm obrigado as organizações a adotarem estratégias que as tornem capazes de enfrentar os desafios que lhes são impostos. No Brasil, o acesso ao ensino universitário, até recentemente era reservado a uma parcela reduzida da população; medidas implantadas a partir de 1996 ampliaram as oportunidades para novos segmentos da população, mediante aumento do número e das características das instituições de ensino superior. Esta pesquisa teve como objetivo analisar as estratégias adotadas por instituições de ensino superior da rede privada que estão enfrentando a competitividade. A pesquisa analisou dados secundários obtidos nos sites do Instituto Nacional de Estudos e Pesquisas Educacionais Anísio Teixeira (INEP), nos relatórios de pesquisas e dados de consultores da área. As instituições estudadas se consideram empresas de educação e expressam a necessidade de obter lucros e garantir a produtividade como fazem empresas de outros setores. Para isto, têm adotado medidas que as levem a evitar os prejuízos, adotando estruturas organizacionais mais simples, mantendo o corpo docente e administrativo enxuto, focando na distribuição mais racional das tarefas administrativas e de ensino

Effect of an endurance training-overtraining protocol on rat muscular oxidative capacity

Overtraining may outcomes for functional overreaching (FOR), a short term decline in performance that leads eventually to an improvement in performance after recovery, or nonfunctional overreaching (NFOR) when performance decline may be reversed only by a longer regenerative period. Recently we developed a training-overtraining protocol for rats with increased workload: eight weeks of daily exercise sessions, followed by three weeks of increasing daily training frequency (2, 3 and 4 times) with decreasing recovery time between sessions (4, 3 and 2h), characterized by analyses of performance before training (T1) and after the 4th(T2), 8th(T3), 9th(T4), 10th(T5) and 11th(T6) training weeks. All rats showed significantly increased performance at T4 and eight rats constitute the trained group (Tr). After T6, two groups were distinguishable by differences in the slope (α) of a line fitted to the individual performances at T4, T5 and T6: NFOR: α\u3c-15.05Kgm and FOR: α≥-15.05Kgm. Our goal was to verify the muscle’s oxidative capacity of Tr, FOR and NFOR groups. Skeletal muscle mitochondrial complexes I, IV and citrate synthase (CS) activity were quantified through Histochemical-staining-BN-PAGE and spectrophotometer analysis, respectively. The area of complexes I and IV was expressed relative to the area for comassie-stained complex V. Significant decreases were found in complex IV (17.2±5.84) and CS activity (22.7±3.21U/gwet) in NFOR group when compared with Tr (35.39±11.33, 32.8±5.24U/gwet) and FOR (28.9±11.37, 31.8±2.75U/gwet). There is a relationship between NFOR and the reduction of muscle oxidative capacity. Thus, aerobic tests should be performed in training routine to monitor performance alterations preventing these situations