The main objective of this thesis is to study the behavior of black objects in external fields, for example black holes and black strings in 4 and 5-dimensional spacetimes respectively. In particular, to analyze how external fields affect horizons and the internal structure of such objects, to study their properties, and tocunderstand how the spacetime fabric works. The thesis contains three chapters. In Chapters 1 and 2 we study the interior of 4-dimensional static, axisymmetric, electrically neutral and electrically charged distorted black holes. We analyze how external static and axisymmetric distortions affect the interior of such black holes. In particular, we study the behavior of the interior solution of an electrically neutral black hole near its horizon and singularity. The analysis shows that there exists a certain duality between the event horizon and the singularity. As a special example, we study the interior of a compactified 4-dimensional Schwarzschild black hole. In the case of an electrically charged black hole, a similar duality exists between its event and Cauchy horizons. The duality implies that the Cauchy horizon remains regular, provided the distortion is regular at the event horizon. Extension of the general theory of relativity to higher dimensional spacetimes brings a large variety of black objects whose boundary, the event horizon, may be of a complicated structure. One such object is a black string. In Chapter 3 we discuss the so-called Gregory-Laflamme instability of 5-dimensional black strings in a spacetime with one compact dimension and their topological phase transitions. Here we consider black strings with electric or magnetic charge. Linear static perturbations of these objects indicate the presence of a threshold unstable mode. An analysis of such mode shows that an electrically charged black string is less stable than a neutral one. The situation is opposite for a magnetically charged black string. An analysis of 5-dimensional extremal black string with electric charge shows a continuous spectrum of unstable threshold modes. The results presented in this thesis may have applications in the theory of classical 4-dimensional black holes and in the modern theoretical models of higher dimensions.

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Orientador: Prof. Dr. Roldão da Rocha Junior / Tese (doutorado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2015. / Revisaremos principalmente modelos de mundos branas em cinco dimensões desde suas ver- sões .nas ou espessas. Em branas .nas revisaremos a formulação de Shiromizu, Maeda e Sasaki e deduziremos as Equações de Einstein efetivas na brana. Veremos que a partir delas podemos veri.car desvios na Relatividade Geral 4D devido à dimensão extra. Analisaremos as implicações diretas na teoria de buracos negros e em alguns aspectos da cosmologia. Ver- emos também um método de expansão que nos permite veri.car a extensão do horizonte de eventos ao bulk, para então introduzirmos cordas negras usando a formulação de Shiromizu, Maeda e Sasaki. Através do método mencionado, mostraremos alguns exemplos que en- volvem dois de nossos trabalhos realizados no período de doutorado. Mostraremos ainda um estudo alternativo que visa analisar as singularidades físicas no bulk oriundas de soluções de colapsos na brana. Referente às branas espessas, faremos uma revisão do modelo canônico visando o estudo de sua estabilidade. Posteriormente, iremos trabalhar a estabilidade do modelo de brana taquiônica. Nesse caso, ainda não se havia veri.cado a estabilidade para o setor de .utuações escalares de maneira geral, mas apenas na aproximação de rolamento lento. Esse resultado é então obtido pela primeira vez. Segue que uma forma de veri.car a estabilidade é observar o espectro das perturbações. Podemos então fazer uso de operadores supersimétricos, que garantem que o espectro é positivo de.nido. Nosso intuito será então veri.car a estabilidade das branas taquiônicas sem qualquer aproximação. Para isso desenvolveremos um mecanismo que envolve operadores supersimétricos de maneira não trivial, sendo uma generalização da literatura pré-existente. O principal resultado obtido é que a brana taquiônica, podendo ela ser de Minkowski ou (anti-) de Siter, é estável diante perturbações escalares. / We will review braneworlds models in .ve dimensions, such as the thin and thick branes cases. In the thin branes context we will review the Shiromizu-Maeda-Sasaki formulation and then we must obtain the e¤ective Einstein equations on the brane. Starting from these equations, we will check some deviations of 4D General Relativity, driven by extra dimension. Some of direct implications will be analyzed for black holes and cosmology. With a perturbative method that provides the event horizon in the bulk, we will introduce the notion of black string in Shiromizu-Maeda-Sasaki formulation. Across of expansion method we will analyze some examples, such as two of our works and then we must .nish with an alternative method for the treatment of singularities on the bulk. Regarding the thick brane, initially we will work the canonical model and posteriorly the tachyon brane model. In the two cases we will develop the stability of models. For the tachyon brane case, the scalar sector has not been studied but only at a slow roll approxima- tion and thus our result is original. The spectra of linear perturbations allows us the study of stability. The use of supersymmetric operators assures us a positive de.ned spectrum. The main objective of this thesis is to check the tachyon brane stability without any ap- proximation. For this purpose we will construct a nontrivial mecanism via supersymmetric operators, which is a generalization of previous literature. The signi.cant result is that the Minkowski, (anti-) de Siter tachyon brane remains stable when perturbed by scalar sector.

This thesis is concerned with several problems in general relativity and low energy string theory that are pertinent to the time evolution of the gravitational field. We present a formulation of the Einstein field equations in terms of variational techniques borrowed from geometric analysis. These equations yield the evolution equations for the Cauchy problems of both general relativity and low energy string theory. We then proceed to investigate the evolutionary linear stability of Schwarzschild-like solutions in higher dimensional relativity called black strings. These objects are determined to be linearly unstable. This motivates a further stability analysis of the charged p-brane solutions of low energy string theory. We show that one can eliminate linear instabilities in p-branes for sufficiently large values of charge. We also consider the characteristic problem of general relativistic magnetohydrodynamics (GRMHD). We compute the eigenvalues and eigenvectors of GRMHD and establish degeneracy conditions. Finally, we consider the initial value problem for axisymmetric GRMHD. We formulate the general Einstein and MHD equations under the assumption of a stationary axisymmetric spacetime without assuming the circularity condition.