This Thesis is concerned with three particular aspects of extended cosmic strings and domain walls in cosmology: their dynamics, gravitation and interaction with a black hole. In Chapter 3, we study the dynamics of an abelian-Higgs cosmic string. We find its equations of motion from an effective action and compare, for three test trajectories, the resulting motion with that observed in the Nambu-Gotō approximation. We also present a general argument showing that the corrected motion of any string is generically antirigid. We pursue the investigation of the dynamics of topological defects in Chapter 5, where we find (from integrability conditions rather than an effective action) the effective equations governing the motion of a gravitating curved domain wall. In Chapter 4 we investigate the spacetime of a gravitating domain wall in a theory with a general potential V(ɸ). We show that, depending on the gravitational coupling e of the scalar ɸ, all nontrivial solutions fall into two categories interpretable as describing respectively domain wall and false vacuum-de Sitter solutions. Wall solutions cannot exist beyond a value (^4)(_3)ɛmax, and vacuum-de Sitter solutions are unstable to decaying into wall solutions below ɛmax at ɛmax we observe a phase transition between the two types of solution. We finally specialize for the Goldstone and sine-Gordon potentials. In Chapter 6 we consider a Nielsen-Olesen vortex whose axis passes through the centre of an extremal Reissner-Nordstr0m black hole. We examine in particular the existence of piercing and expelled solutions (where the string respectively does and does not penetrate the black hole's horizon) and determine that while thin strings penetrate the horizon — and therefore can be genuinely called hair — thick strings are expelled; the two kinds of solution are separated by a phase transition.

With the start of the age of the Large Hadron Collider (LHC) two challenges face theoreticians and computational physicists. The first is about understanding theories beyond the Standard Model and producing verifiable predictions that can be tested against what the LHC and subsequent machines would produce. The second is to improve computational methods so that the new experimental precision is matched by a theoretical one. But this improvement is also crucial for the detection of potential deviations from Standard Model predictions and possibly also finding the elusive Higgs. This work tries to address problems in both areas. In the first part we study the effects of adding tension in considering a black-hole on a brane. Such black-holes are predicted by some models as potential phenomena at the LHC. We calculate the effects of adding tension on observable quantities of black-holes, namely, quasinormal mode frequencies and Hawking radiation, and we show how this improves predictions. In the second part we investigate the computational problem of extending the Britto-Cachazo-Feng-Witten (BCFW) method to 1-loop level. The BCFW has been successfully used in recent years to compute scattering amplitudes at tree-level by suitably complex-shifting external momenta and reducing diagrams to simpler ones. In our investigation we establish that the BCFW can be extended to 1-loop, which means that 1-loop integrands can be treated as trees and can be broken down further into even simpler trees using the BCFW. We explicitly look at the effects of the shift for the lowest three n-point cases, but also demonstrate how the result extends to arbitrary n.

The fuzzball model of a black hole is an attempt to resolve the many paradoxes and puzzles of black hole physics that have revealed themselves over the last century. These badly behaved solutions of general relativity have given physicists one of the few laboratories to test candidate quantum theories of gravity. Though little is known about exactly what lies beyond the event horizon, and what the ultimate fate of matter that falls in to a black hole is, we know a few intriguing and elegant semi-classical results that have kept physicists occupied. Among these are the known black hole entropy and the Hawking radiation process.

Des trous noirs supermassifs de plusieurs centaines de millions de masses solaires résident au centre de la plupart des galaxies massives. Dans 90% des cas, ces trous noirs sont dans état quiescent, très peu lumineux. Cependant, dans les 10% restant, des processus extrêmement violents sont observés, avec la libération d'énorme quantités d'énergie no- tamment en UV, X et gamma. On observe aussi parfois des jets puissants de matière pouvant s'étendre sur plusieurs centaines de kpc. Le coeur de ces galaxies sont appelés Noyaux Actifs de Galaxie (NAG). Ce sont parmis les objets les plus lumineux de l'univers. L'accrétion de la matière environnante sur le trou noir supermassif central est unanimement reconnue comme la source d'énergie la plus plausible pour expliquer la puissance phénoménale observée. L'énergie gravitationelle serait ainsi en partie libérée dans un disque d'accrétion, sous forme de rayonnement thermique piquant dans l'optique/UV, et en partie rayonnée en X/gamma par une couronne de plasma chaud présente dans l'environnement proche du trou noir.De nombreux phénomènes sont néanmoins encore très mal connus et beaucoup de ques- tions n'ont toujours pas de réponses satisfaisantes: quelles sont la dynamique et la structure des flots d'accrétion et d'éjection dans les NAG? Quels sont les processus radiatifs produisant le rayonnement UV/X? Quelle est l'origine des différentes composantes spectrales présentes dans ces domaines d'énergie? Cette thèse a pour objectif d'apporter de nouvelles contraintes observationnelles pour meux répondre à ces questions. Son originalité réside dans le développement et l'utilisation de modèles réalistes de Comptonisation thermique permettant d'une part de mieux contraindre les propriétés physiques et géométriques des régions d'émission UV/X et d'autre part de mieux comprendre l'origine des différentes composantes spectrales observées. Nous nous sommes notamment intéressés, au cours de cette thèse, à l'excès d'émission X-mou (<2 keV), présent dans un grand nombre de NAG, et dont l'origine est toujours inconnue.Ces travaux s'articulent autour de deux axes principaux. Le premier est l'étude spectrale détaillée de longues campagnes d'observation multi-longueur d'ondes de trois galaxies de Seyfert (NGC 5548, NGC 7213 et NGC 4593). La qualité des données ont ainsi permis de révéler les paramètres physiques (notamment la température et la profondeur optique) et géométriques de la couronne thermique à l'origine du continuum X. Le second axe porte sur l'analyse de données d'archives (en provenance du satellite XMM-Newton) d'un échantillon important de galaxies de Seyfert. Cela a permis d'apporter, cette fois ci, des contraintes plus générales sur les processus d'émission haute énergie observés dans ces objets. Ces deux approches ont notamment montré que l'exces d'émission X-mou pouvait provenir des couches supérieures chaudes du disque d'accrétion, suggérant un chauffage plus efficace en surface plutôt que dans les régions internes. / Supermassive black holes of several hundred million solar masses lie at the centre of most massive galaxies. In 90% of cases, these black holes are in quiescent, very low luminous states. Nevertheless, in the remaining 10%, extremely violent processes are seen, with the liberation of huge amounts of energy especially in the UV, X-ray and gamma-ray bands. We also sometimes observe powerful jets, extending up to several hundred kpc scales. The cores of these galaxies are called Active Galactic Nuclei (AGNs). These are among the most luminous objects in the Universe. The accretion of surrounding matter onto the central supermassive black hole is generally considered as the most likely energy source to explain the extraordinary observed luminosity. The gravitational energy would be partly liberated into an accretion disc as thermal radiation peaking in the optical/UV band, and partly radiated in the X-ray/gamma-ray band by a corona of hot plasma lying in the environment close to the black hole.However, several phenomena are still poorly understood and a number of questions lacks satisfactory answers: what are the dynamics and the structure of the accretion and ejection flows in AGNs? What are the radiative processes producing the UV/X-ray radiation? What is the origin of the different spectral components present in those energy bands? The goal of this thesis is to derive new observational constraints to better answer to these questions. Its originality resides in the development and application of realistic models of thermal Comptonization, allowing on the one hand to better constrain the physical and geometrical properties of the UV and X-ray-emitting regions, and on the other hand to better understand the origin of the different observed spectral components. In particular, we studied the excess of the soft (<2 keV) X-ray emission, seen in a great number of AGNs, and whose origin is still unknown.This work is structured along two main branches. One is the detailed spectral analysis of long, multiwavelength observational campaigns on three Seyfert galaxies (NGC 5548, NGC 7213 and NGC 4593). The quality of the data permitted to reveal the geometrical and physical parameters (in particular the temperature and optical depth) of the thermal corona producing the X-ray continuum. The second branch is based on the analysis of archival data (from the XMM-newton satellite) of a large sample of Seyfert galaxies. This allowed us to derive more general constraints on the high-energy emission processes observed in these objects. These two approaches have shown, in particular, that the soft X-ray emission excess may arise in the warm upper layers of the accretion disc, suggesting a more effective heating of the surface rather than the inner regions.

Dans cette thèse, nous explorons la phénoménologie de certaines extensions de la relativité générale et de la gravité quantique.Cette recherche est motivée par l’incomplétude des modèles théoriques qui décrivent le comportement de la matière aux échelles cosmologiques.Le model standard de la physique des particules et la relativité générale, combinés ensemble et avec les données expérimentales provenant des collisionneurs de particules et de l’astrophysique, conduisent a des modèles d’univers domines par de la matière invisible. De plus, selon le meilleur de ces modèles, l’univers serait présentement dans une phase d’expansion accélérée et aurait commencer son existence par une singularité spatio-temporelle : le big bang.Ainsi, la physique théorique se trouve mise au défi d’obtenir un model sans singularités et avec moins (ou aucune) matière sombre. Sur ce point, les deux dernières décennies ont étés particulièrement fructueuse : il y a maintenant un grand nombre de théories de gravité modifiée, d’énergie sombre et de gravité quantique qui sont à notre disposition.L’objectif du présent travail est de construire un cadre phénoménologique nous permettant de comparer clairement ces théories les unes aux autres et possiblement d’en réfuter certaines en se basant sur les récentes observations cosmologiques ainsi que celles qui sont encore a venir.La première partie de la thèse est dédiée aux théories de gravité modifiée et d’énergie sombre. La deuxième partie traite de la cosmologie quantique a boucles, et finalement la dernière partie présente une nouvelle façon de sonder l’expansion accélérée de l’univers via l’effet Sunyeav Zeldovich thermique. / In this thesis we explore the phenomenology of some extensions to General Relativity and quantum gravity theories.The motivation for this research lies in the incompleteness of the current theoretical models that describe the behaviour of matter on cosmological scales.The standard model of particle physics and general relativity, combined together along with experimental probes in particle colliders and astrophysics, lead to a model for our universe, which is today dominated by dark matter. Moreover, according to the best model, the universe is currently undergoing an accelerated expansion and had started its existence with a space-time singularity: the big bang.The challenge for theoretical physics is therefore to obtain a model without singularity and with less invisible matter (or none). To this respect, the last two decades have been particularly fruitful: there is a large number of competing modified gravity and dark energy theories as well as quantum gravity proposals at our disposal.The purpose of the work presented here is to set up a phenomenological framework that enables a clear comparison and possible exclusions of these new theories by confronting them to current and future observational data.The first part of the thesis is dedicated to modified gravity and dark energy models. The second part deals with loop quantum cosmology, and the last part is a presentation of a new probe for dark energy: the thermal Sunyaev Zeldovich power spectrum.

Submitted by Emanuel Varela Cardoso (emanuel.varela@ufcg.edu.br) on 2018-10-17T17:33:09Z No. of bitstreams: 1 Dissertação-Ildemar Barreto Veloso -(OK).pdf: 627444 bytes, checksum: ba9ac192a954812365d05a8c75c86647 (MD5) / Made available in DSpace on 2018-10-17T17:33:09Z (GMT). No. of bitstreams: 1 Dissertação-Ildemar Barreto Veloso -(OK).pdf: 627444 bytes, checksum: ba9ac192a954812365d05a8c75c86647 (MD5) Previous issue date: 2016-09 / Capes / A Relatividade Geral, que foi construída baseada nos princípios da equivalência e da covariância,é a teoria da gravitação que admite um espaço-tempo não euclidiano. Ela permite que o espaço-tempo se torne curvo próximo à distribuições de matéria. Os buracos negros são objetos com imensas concentrações de matéria, que provocam grandes perturbações no espaço a sua volta. A métrica correspondente ao buraco negro que analisamos foi a de Schwarzschild. Tais objetos também podem ser analisados utilizando-se a termodinâmica, com a obtenção de variáveis como temperatura e entropia. Este último conceito, é de fundamental importância para entendermos a questão do emaranhamento entre dois sistemas físicos correlacionados e a teoria de informação. Assim, nosso objetivo foi analisar alguns fatores sobre o paradoxo da conservação da informação em buracos negros. Além do mais, também analisamos como o emaranhamento entre duas regiões desconectadas pode gerar espaços-tempos conectados, e qual sua relação com as pontes deEinstein-Rosen. / The General Relativity, that was built on the equivalence and covariance principles, is the gravitation the or which admits an on-euclide an space time. It permits that the space time be comes curve near matter distributions. The black holes are objects with huge concentrations of matter, which cause major disruption in the space around it.The corresponding metric to the black hole that were view edit is the Schwarzschildmetric. Such objects canal sobe analyzed using the thermo dynamic concepts, to obtain variables such as temperature and entropy. This one, will be of fundamental importance to understanding the question of the entanglement between two related physical systems and the concept of information. So, ourgo alitis to examine some factors aboutt he information conservation paradox in black holes. Moreover, also we analyzedas a entan- glement between two disconnected regions can generate space time connected,and what is its relationship with Einstein-Rosenbridges.

BALTAZAR, H. I. Métricas críticas do funcional volume e não-existência de múltiplos buracos negros em espaço-tempo estático. 2017. 67 f. Tese (Doutorado em Matemática) – Centro de Ciências, Universidade Federal do Ceará, Fortaleza, 2017. / Submitted by Andrea Dantas (pgmat@mat.ufc.br) on 2017-07-12T19:24:59Z No. of bitstreams: 1 2017_tese_hibaltazar.pdf: 449308 bytes, checksum: a4275b6fceeb5cb76fe217e956f933cd (MD5) / Approved for entry into archive by Rocilda Sales (rocilda@ufc.br) on 2017-07-13T12:17:45Z (GMT) No. of bitstreams: 1 2017_tese_hibaltazar.pdf: 449308 bytes, checksum: a4275b6fceeb5cb76fe217e956f933cd (MD5) / Made available in DSpace on 2017-07-13T12:17:46Z (GMT). No. of bitstreams: 1 2017_tese_hibaltazar.pdf: 449308 bytes, checksum: a4275b6fceeb5cb76fe217e956f933cd (MD5) Previous issue date: 2017-07-05 / This work is divided in two parts. In the first one we prove a Böchner type formula for critical metrics of the volume functional on compact manifolds with fixed metric on boundary (such critical metrics are called Miao-Tam critical metrics). As an application, we derive an integral formula that will be crucial to deduce a generalization of a result obtained by Miao and Tam in 2011 for the Einstein case. More precisely, we prove that a Miao-Tam critical metric with parallel Ricci curvature must be isometric to a geodesic ball in a simply connected space form Rn, Sn or Hn. Furthermore, in dimension 3, we prove that critical metrics with non-negative sectional curvature are precisely geodesic balls of R3 or S3. Moreover, we generalize a result due to Kim and Shin (2016), replacing the harmonic Weyl tensor condition by the second order divergence free Weyl tensor condition (i.e., div2W = 0), which is weaker that the former. To be precise, we shall show that a 4-dimensional Miao-Tam critical metric, with boundary isometric to a standard sphere S3 and satisfying div2W = 0 is isometric to a geodesic ball in a simply connected space form R4, S4 or H4. At the same time, we get some rigidity results for positive static triples. In the second part, we study static vacuum space-times, which can be seen as a special case of the V-static metrics for complete Riemannian manifolds with null scalar curvature. In this case, we focus our attention on four dimensions. We prove that there are no multiple black holes on static vacuum space-times with half harmonic Weyl tensor (i.e., divW+ = 0). / Esse trabalho está dividido em duas partes. A primeira delas está relacionada ao estudo de fórmulas tipo-Böchner para métricas críticas do funcional volume em variedades compactas com métrica fixada no bordo (estas são conhecidas como métricas críticas de Miao-Tam). Como aplicação, estabeleceremos uma fórmula integral que permitirá generalizar o resultado obtido por Miao e Tam em 2011 para o caso Einstein, mais precisamente, provaremos que métricas críticas de Miao-Tam com curvatura de Ricci paralelo são isométricas às bolas geodésicas em um espaço forma simplesmente conexo Rn, Sn ou Hn. Se nos restringirmos às variedades com dimensão 3, veremos que tais estruturas se mostram ainda mais rígidas, a saber, provaremos que métricas críticas com curvatura seccional não-negativa são precisamente as bolas geodésicas de R3 ou S3. Além disso, generalizamos o resultado obtido por Kim e Shin (2016) substituindo condição de harmonicidade do tensor de Weyl pela hipótese que o tensor de Weyl tem divergente de segunda ordem nulo (i.e., div2W = 0). Mais precisamente, mostraremos que métricas críticas de Miao-Tam em dimensão 4, com bordo isométrico a esfera S3 e satisfazendo div2W = 0, são isométricas às bolas geodésicas em um espaço forma simplesmente conexo R4, S4 ou H4. Concomitantemente, obtemos resultados de rigidez para triplas estáticas positivas. Na segunda parte do trabalho, estudaremos o espaço-tempo estático no vácuo, o qual pode ser visto como um caso especial das mátricas V-estáticas para variedades completas com curvatura escalar nula. Neste caso, restringiremos nosso estudo a quarta dimensão e provaremos que não existem múltiplos buracos negros em um espaço-tempo estático no vácuo com a parte autodual do tensor de Weyl harmônico (i.e., divW+ = 0).

Conselho Nacional de Desenvolvimento Científico e Tecnológico / The electromagnetic and gravitational quasinormal mode spectra of plane-symmetric anti-de Sitter black holes are investigated in the present work. According to the AdS/CFT correspondence, the black hole quasinormal frequencies correspond to the poles of R-current and stress-energy tensor correlation functions in the holographically dual field theory: the N = 8 super-Yang-Mills in 2 + 1 dimensions. In the present study, this duality is explored in order to choose the quasinormal mode boundary conditions and the gauge invariant variables governing the black hole perturbations. Among the main results, it is shown that zero wavenumber axial perturbations yield only small rotations on the system, while the polar perturbations lead to a change in the mass of the black hole and may also produce cylindrical gravitational waves. In relation to the quasinormal spectra, the long-distance and low-frequency limit of the dispersion relations present the hydrodynamical behavior that is characteristic of a conformally invariant theory, with diffusion, shear and sound-wave modes. In the electromagnetic perturbation sector, it also appears purely damped modes that tend to the bosonic Matsubara frequencies in the long-wavelength regime. / No presente trabalho, investigou-se o espectro de vibrações eletromagnéticas e gravitacionais de buracos negros anti-de Sitter com horizontes plano-simétricos. Segundo a correspond ência AdS/CFT, os modos quase-normais desses buracos negros estão associados aos pólos de funções de correlação de corrente-R e do tensor energia-momento na teoria de campos holograficamente dual: a super-Yang-Mills N = 8 em 2 + 1 dimensões. Neste estudo, a relação com a teoria de campos foi explorada ao se fixar as condições de contorno que definem os modos quase-normais, bem como na escolha das quantidades invariantes de calibre que governam as perturbações dos buracos negros anti-de Sitter. Para obter as equações de onda gravitacionais, foram utilizados formalismos baseados em variações da métrica e dos escalares de curvatura de Weyl. Entre outros resultados, mostrou-se que as perturbações axiais com número de onda nulo produzem somente pequenas rotações sobre o sistema, enquanto que as perturbações polares conduzem a mudanças na massa e também podem se propagar na forma de ondas gravitacionais cilíndricas. Em relação ao espectro quase-normal, no limite de baixas freqüências e grandes comprimentos de onda, algumas relações de dispersão apresentam o comportamento hidrodinâmico característico de uma teoria conformemente invariante, com o aparecimento de modos de difusão, cisalhamento e de onda sonora. Por fim, no setor eletromagnético das perturbações, surgem também modos puramente amortecidos que tendem às freqüências de Matsubara de um sistema bosônico no regime de grandes comprimentos de onda.

Submitted by Gabriel Cozzella (cozzella@ift.unesp.br) on 2016-08-21T00:22:31Z No. of bitstreams: 1 MSc Dissertation.pdf: 773902 bytes, checksum: a2d2f3173a5f3ec0ab24f201d71929da (MD5) / Approved for entry into archive by Ana Paula Grisoto (grisotoana@reitoria.unesp.br) on 2016-08-24T16:43:46Z (GMT) No. of bitstreams: 1 cozzella_g_me_ift.pdf: 773902 bytes, checksum: a2d2f3173a5f3ec0ab24f201d71929da (MD5) / Made available in DSpace on 2016-08-24T16:43:46Z (GMT). No. of bitstreams: 1 cozzella_g_me_ift.pdf: 773902 bytes, checksum: a2d2f3173a5f3ec0ab24f201d71929da (MD5) Previous issue date: 2016-07-26 / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / A teoria quântica de campos em espaços-tempos curvos é o arcabouço teórico mais sólido que temos para estudar a interação entre gravitação e mecânica quântica na ausência de uma teoria completa de gravitação quântica. Neste contexto, um problema que atraiu muita atenção dos físicos teóricos nas últimas décadas é o chamado “paradoxo da perda de informação em buracos negros”, onde a evolução de um estado quântico puro inicial para um estado quântico misto final caracterizaria uma violação das leis da mecânica quântica. Nesta dissertação nós argumentamos que a perda de informação em si não viola as leis da mecânica quântica e é consequência direta da teoria semi-clássica utilizada. Finalmente, argumentamos que a questão da recuperação da informação deve ser tratada utilizando-se uma teoria de gravitação quântica ainda desconhecida. / The quantum theory of fields in curved space-times is the most solid framework for studying the interplay between gravity and quantum mechanics in the absence of a complete theory of quantum gravity. In this scenario, one problem that has drawn much attention from the theoretical physics community in the last decades is the so-called “black hole information loss paradox”, where the evolution from an initial pure quantum state to a final mixed quantum state would constitute a violation of the laws of quantum mechanics. In this dissertation we argue that information loss does not violate quantum mechanics, being simply a consequence of the semi-classical framework adopted and that the question of information recovery needs to be addressed by a yet unknown theory of quantum gravity. / FAPESP: 2014/08684-9

Made available in DSpace on 2015-05-14T12:14:12Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 2241811 bytes, checksum: d494ba9e01bd7d249facca38063cf6ba (MD5) Previous issue date: 2014-04-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / Theories of extra dimensions have been extensively studied in recent years with the original intention of solving the hierarchy problem. Among the models of extra dimensions we can mention the braneworld models, more precisely, the Randall-Sundrum model, which considers our universe as a brane embedded in an ambient space with an extra dimension of infinite size. The fundamental aspect of the brane models is that matter and fields are confined in a hypersurface and only gravity has access to all dimensions. Thus, observational tests involving gravity may provide a way of verifying the existence of extra dimensions. With this idea in mind, in this work, we find black hole solutions in a regularized version of a RSII type brane and then we consider two classical tests of general relativity to these solutions. We studied the in uence of transversal movement in the four-dimensional path of the particles. We note that the de ection of light and the time delay, in this scenario, depend on the energy ( frequency ) of the light signal and can, therefore, give rise to the phenomenon of gravitational rainbow. We also discuss a model of thick branes known as the split fermion model. In this model electrons and protons are located on di¤erent hypersurfaces of the brane. We found that, in the presence of a gravitational eld generated by a massive body, these particles will experience di¤erent four-dimensional geometries. This violation of the equivalence principle, from the viewpoint of four-dimensional observers, produces interesting phenomena as, for instance, the gravitational induction of an electric dipole in a hydrogen atom. We veri ed that the Hamiltonian that describes this e¤ect has the same form of the Stark Hamiltonian, i.e., H = ~A ~r, where the tidal acceleration ~A(due to the separation of electron and proton in the extra dimension) substitutes the electric eld and the reduced mass atom replaces the electric charge. / Teorias de dimensões extras têm sido amplamente estudadas nos últimos anos, com o intuito original de resolver o problema da hierarquia. Entre os modelos de dimensões extras podemos citar o modelo de branas Randal-Sundrum, que trata o nosso universo como uma brana imersa em um espaço ambiente com uma dimensão extra de comprimento infinito. O aspecto fundamental do cenário de branas é que a matéria e os campos estão confinados em uma hipersuperfície e, apenas, a gravidade tem acesso a todas as dimensões. Sendo assim, testes observacionais envolvendo a gravitação podem oferecer meios de se verificar a existência das dimensões extras. Com esta ideia em mente, neste trabalho, encontramos soluções de buracos negros em uma versão regularizada de uma brana (ou seja, com espessura) do tipo RSII e aplicamos, então, dois testes clássicos da relatividade geral para estas soluções de buracos negros, estudando a influência do movimento transversal nas trajetórias quadrimensionais das partículas. Constatamos que o desvio da luz e o atraso temporal, neste cenário, passam a depender da energia (frequência) do sinal luminoso, podendo, portanto, dar origem ao fenômeno de arco-íris gravitacional. Discutimos também um modelo de branas com espessura, conhecido como modelo de separação de férmions, formulado com o propósito de explicar a estabilidade do próton sem recorrer a algum tipo de simetria. Neste modelo, elétrons e prótons estão localizados em diferentes hipersuperfícies da brana. Verificamos que na presença de um campo gravitacional gerado por um corpo massivo, estas partículas irão sentir diferentes geometrias quadrimensionais. Esta aparente violação do princípio da equivalência, do ponto de vista de observadores quadrimensionais, produz interessantes fenômenos como, por exemplo, a indução, pela gravidade, de um dipolo elétrico em um átomo de Hidrogênio. Verificamos que a Hamiltoniana que descreve este efeito tem a mesma forma da Hamiltoniana de Stark, ou seja, H = ~A ~r, onde a aceleração de maré ~A (devido à separação de elétron e próton na dimensão extra) está no lugar do campo elétrico e a massa reduzida do átomo substitui a carga elétrica.