<p>This dissertation focuses on emergent geometry from SU(1,1) dynamical symmetry and non-Hermitian physics. While the geometrical approach unifies distinct phenomena in Hermitian and non-Hermitian systems, it also provides distinct means of coherent control of quantum dynamics and simulating exotic spacetimes.</p>

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We study a free quantum scalar field in the BTZ spacetime as a model of the AdS/CFT correspondence for black holes, and show the essential steps in computing Bogolyubov coefficients between modes on either side of the wormhole. As background, we review the BTZ geometry in standard, Kruskal and Poincaré coordinates, holographic renormalisation of the dual field theory and canonical quantisation in curved spacetime. / Vi studerar ett fritt skalärt kvantfält i BTZ-rumtiden som en modell av AdS/CFT-dualiteten för svarta hål och visar huvudstegen i beräkningen av Bogolyubov-koefficienter mellan moder på olika sidor av maskhålet. Som bakgrund redogör vi för BTZ-geometrin i standard-, Kruskal- och Poincarékoordinater, holografisk renormering av den duala fältteorin och kanonisk kvantisering i krökt rumtid.

Thesis (MSc)--Stellenbosch University, 2013. / ENGLISH ABSTRACT: In this thesis I study compact objects described by the Manko-Novikov spacetime. The Manko- Novikov spacetime is an exact solution to the Einstein Field Equations that allows objects to be black hole-like, but with a multipole structure di erent from Kerr black holes. The aim of the research is to investigate whether we will observationally be able to tell these bumpy black holes, if they exist, apart from traditional Kerr black holes. I explore the geodesic motion of a test probe in the Manko-Novikov spacetime. I quantify the motion using Poincar e maps and rotation curves. The Manko-Novikov spacetime admits regions with regular motion as well as regions with chaotic motion. The occurrence of chaos is correlated with orbits for which the characteristic frequencies are resonant. The new result presented in this thesis is a global characterisation of where resonances and thus chaos are likely to occur for all orbits. These calculations are performed in the Kerr spacetime, from which I obtain that low order resonances occur within 20 Schwarzschild radii (or 40M) of the compact object with mass M. By the KAM theorem, the occurrence of chaos is therefore limited to this region for all small perturbations from Kerr. These resonant events will be measurable in the Galactic Centre using eLISA. This con nement of low order resonances indicates that the frequency values of orbits of radii well outside of 20 Schwarzschild radii can be approximated using canonical perturbation theory. / AFRIKAANSE OPSOMMING: In hierdie tesis word kompakte voorwerpe bestudeer soos omskryf deur die Manko-Novikov ruimtetyd. Die Manko-Novikov ruimtetyd is 'n eksakte oplossing van die Einstein Veldvergelykings. Die Manko-Novikov ruimtetyd formuleer gravitasiekolk-tipe voorwerpe waarvan die veelpool-struktuur afwyk van die tradisionele Kerr gravitasiekolk-struktuur. Die oogmerk van die navorsing is om vas te stel of ons met behulp van waarnemings hierdie bonkige gravitasiekolke van die tradisionele Kerr gravitasiekolke kan onderskei. Ek ondersoek die geodetiese beweging van 'n toetsmassa in die Manko-Novikov ruimtetyd. Die beweging word gekwanti seer met behulp van Poincar e afbeeldings en rotasiekrommes. In die Manko-Novikov ruimtetyd identi seer ek gebiede waarbinne re elmatige beweging voorkom asook gebiede waarbinne chaotiese bane voorkom. Die ontstaan van chaos word geassosieer met bane waarvan die fundamentele frekwensies resonant is. 'n Nuwe resultaat wat in hierdie tesis voorgehou word behels 'n globale karakterisering wat aandui waar resonansies en dus chaos na alle waarskynlikheid voorkom. Laasgenoemde berekeninge word vir die Kerr ruimtetyd uitgevoer. Hierdeur toon ek alle lae orde resonansies kom voor binne 20 Schwarzschild radii (of 40M) vanaf die kompakte voorwerp met mass M. Die KAM Stelling bepaal dan dat vir alle klein steurings toegepas op die Kerr ruimtetyd die voorkoms van chaos beperk sal wees tot bogenoemde gebied. Die resonansies binne hierdie gebied sal deur eLISA in die sentrum van die melkwegstelsel gemeet kan word. Hierdie beperking van lae orde resonansies tot 'n sekere afstand vanaf die kompakte voorwerp verseker dat die frekwensies van bane wat buite hierdie gebied val, akkuraat deur kanoniese steuringsteorie bepaal kan word.

As propriedades termodinâmicas relacionadas a um gás composto por partículas bosônicas em geometrias esfericamente simétricas são apresentadas ao longo deste trabalho. Utilizando o formalismo proposto por Ishibashi e Kodama, verificou-se que as equações de movimento associadas aos campos escalar e eletromagnético podem ser reduzidas a uma equação tipo Schrödinger. Ao considerarmos algumas soluções esfericamente simétricas observou-se que o espectro de energia associado às partículas é discretizado. Em particular, no estudo das lightspheres, superfícies onde os fótons estão confinados em órbitas fechadas, propomos um mecanismo de quantização para as partículas bosônicas. Estudamos algumas propriedades termodinâmicas e dentro deste tratamento, é apresentada uma expressão para a densidade de energia espectral da radiação emitida. Nossos resultados sugerem que as lightspheres quando termalizadas com o seu ambiente, possuem propriedades termodinâmicas não-usuais. Ao levarmos em consideração a presença da constante cosmológica negativa, constatou-se que além de um espectro de energia discretizado, a geometria adS possui um comportamento confinante, podendo ser interpretada como uma caixa de tamanho conhecido. Considerando um gás de partículas bosônicas confinadas na geometria anti-de Sitter, obtivemos as grandezas termodinâmicas associadas tais como energia interna, entropia e pressão. Para a energia interna observamos um comportamento diferente do usual para o limite de baixas temperaturas. / The thermodynamic properties related to a gas composed of bosonic particles in spherically symmetrical geometries are presented in this work. Using the formalism proposed by Ishibashi and Kodama, we have seen that the equations of motion associated to the scalar and electromagnetic fields can be reduced to a Schrödinger-like equation. For some spherically symmetrical solutions it has been demonstrated that the energy spectrum associated with the particles is discretized. In particular, when we considered lightspheres, surfaces where photons are confined in closed orbits, we propose a quantization procedure for the bosonics particles. In this treatment, it is presented an expression for the spectral energy density of the emmited radiation. Our results suggest that lightspheres thermalized with its environment, have unusual thermodynamical properties. When taken into account the presence of the negative cosmological constant, it has been shown that, besides a discretized energy spectrum, the geometry has a confining behavior and can be interpreted as a finite size box. Considering a gas of bosonic particles confined in the anti-Sitter geometry, we obtained the associated thermodynamics quantities such as internal energy, entropy and pressure. For the internal energy, in the low temperatures limit, we observe a different behavior from the usual one.

In this work, we review three topics which are relevant on its own but which are also interconnected through the AdS/CFT correspondence: (i) black holes in AdS and its thermodynamics, (ii) nonlinear instability of AdS and (iii) scalar- tensor theory of gravity. Each one of these topics find applications in holography using the above mentioned correspondence. We review the various coordinate systems used to write the AdS metric and discuss the main black holes with AdS asymptotics as well as their thermodynamical properties. We also review current results on linear and nonlinear stability for various spacetimes, presenting a heuristic explanation for the nonlinear instability of AdS. The discussion about alternative theories of gravity is restricted to the case of scalar-tensor theories (Horndeski theories, specially). We study the multipole expansion of the electromagnetic field in the solitonic background of a shift-symmetric scalar-tensor model (up to second order in the scalar field coupling constant with the Gauss-Bonnet term). We find that the multipoles are everywhere regular and finite except for the monopole l = 0, which diverges at the origin of the spacetime coordinates. / Neste trabalho, temos como objetivo fazer uma revisão sobre três temas de grande relevância por si só mas, que também se interligam através da correspondencia AdS/CFT: (i) buracos negros em AdS e sua termodinâmica, (ii) a instabilidade não-linear de AdS e (iii) teorias escalar-tensoriais da gravidade. Cada um destes temas encontram aplicações em holografia usando a correspondencia citada acida. Revisamos as diversas formas de escrever a métrica de AdS e discutimos os principais buracos negros assintóticamentes AdS assim como suas propriedades termodinâmicas. Nós também revisamos os resultados atuais sobre a estabilidade linear e não-linear para diversos espaços-tempos, reproduzindo uma explicação heurísitca sobre a instabilidade não-linear do espaço-tempo AdS. A discussão das teorias alternativas à Relatividade Geral é restrita ao caso das teorias escalar-tensorias da gravidade (a teoria de Horndeski, especialmente). Nós estudamos a expansão multipolar do campo electromagnético em um espaço-tempo que é solução do modelo \"shift-symmetric scalar tensor gravity\" (até segunda ordem na constante de acoplamento do campo escalar com o termo de Gauss-Bonnet) com características solitônicas. Encontramos que os multipolos são regulares e finitos em todo espaço-tempo com exceção do monopolo l = 0, que diverge na origem do sistema de coordenadas.

The aim of this work is present the phenomenon denoted entanglement harvesting. We begin by introducing entanglement historically. Following, we go beyond the one particle theory in flat spacetime and introduce Quantum Field Theory in Curved Spacetime, showing two famous consequences: the Unruh effect and the Hawking radiation. Finally, we analyze entanglement harvesting for two Unruh-deWitt detectors. In the fisrt example, we see that there is a \"sudden death\" point of entanglement harvesting when the detectors are near the BTZ black hole event horizon, due to redshift effect and Hawking radiation. Then, we compare the phenomenon for different scenarios, and find out that it is sensitive to the structure of spacetime. Finally, we see how detectors\' parameters affect it and find out that the smoothness of the switching of the detectors\' coupling to the field is extremely relevant. We also see how the parameters can be used to optimize entanglement harvested. / O objetivo desse trabalho é apresentar o fenômeno denotado colheita de emaranhamento. Primeiramente fazemos uma introdução histórica de emaranhamento de estados quânticos. Em seguida, introduzimos a Teoria Quântica de Campos no Espaço-tempo Curvo, como um passo além da teoria quântica de uma partícula no espaço-tempo plano, e demonstramos dois resultados famosos da teoria: o efeito Unruh e a radiação Hawking. Por fim, fazemos uma analise do fenômeno de colheita de emaranhamento para dois detectores Unruh-deWitt. Nosso primeiro exemplo mostra que há um ponto de \"morte súbita\" do fenômeno quando os detectores se aproximam do horizonte de eventos de um buraco negro de BTZ, que é uma consequência do efeito de redshift e da radiação Hawking. Em seguida, comparamos o fenômeno em cenários diferentes, e observamos que a colheita de emaranhamento é sensível à estrutura do espaço-tempo. Por último, analisamos como os parâmetros dos detectores afetam a colheita de emaranhamento, e vemos que a suavidade em que o acoplamento dos detectores com o campo é \"ligado\" e \"desligado\" é extremamente relevante. Também analisamos como podemos usar os parâmetros dos detectores para otimizar a quantidade de emaranhamento colhida.

No description available.

Famously, Einstein read off the geometry of spacetime from Maxwell's equations. Today, we take this geometry that serious that our fundamental theory of matter, the standard model of particle physics, is based on it. However, it seems that there is a gap in our understanding if it comes to the physics outside of the solar system. Independent surveys show that we need concepts like dark matter and dark energy to make our models fit with the observations. But these concepts do not fit in the standard model of particle physics. To overcome this problem, at least, we have to be open to matter fields with kinematics and dynamics beyond the standard model. But these matter fields might then very well correspond to different spacetime geometries. This is the basis of this thesis: it studies the underlying spacetime geometries and ventures into the quantization of those matter fields independently of any background geometry. In the first part of this thesis, conditions are identified that a general tensorial geometry must fulfill to serve as a viable spacetime structure. Kinematics of massless and massive point particles on such geometries are introduced and the physical implications are investigated. Additionally, field equations for massive matter fields are constructed like for example a modified Dirac equation. In the second part, a background independent formulation of quantum field theory, the general boundary formulation, is reviewed. The general boundary formulation is then applied to the Unruh effect as a testing ground and first attempts are made to quantize massive matter fields on tensorial spacetimes. / Bekanntermaßen hat Albert Einstein die Geometrie der Raumzeit an den Maxwell-Gleichungen abgelesen. Heutzutage nehmen wie diese Geometrie so ernst, dass unsere fundamentale Materietheorie, das Standardmodell der Teilchenphysik, darauf beruht. Sobald es jedoch um die Physik außerhalb des Sonnensystems geht, scheinen einige Dinge unverstanden zu sein. Unabhängige Beobachtungsreihen zeigen, dass wir Konzepte wie dunkle Materie und dunkle Energie brauchen um unsere Modelle mit den Beobachtungen in Einklang zu bringen. Diese Konzepte passen aber nicht in das Standardmodell der Teilchenphysik. Um dieses Problem zu überwinden, müssen wir zumindest offen sein für Materiefelder mit Kinematiken und Dynamiken die über das Standardmodell hinaus gehen. Diese Materiefelder könnten dann aber auch durchaus zu anderen Raumzeitgeometrien gehören. Das ist die Grundlage dieser Arbeit: sie untersucht die zugehörigen Raumzeitgeometrien und beschäftigt sich mit der Quantisierung solcher Materiefelder unabhängig von jeder Hintergrundgeometrie. Im ersten Teil dieser Arbeit werden Bedingungen identifiziert, die eine allgemeine tensorielle Geometrie erfüllen muss um als sinnvolle Raumzeitgeometrie dienen zu können. Die Kinematik masseloser und massiver Punktteilchen auf solchen Raumzeitgeometrien werden eingeführt und die physikalischen Implikationen werden untersucht. Zusätzlich werden Feldgleichungen für massive Materiefelder konstruiert, wie zum Beispiel eine modifizierte Dirac-Gleichung. Im zweiten Teil wird eine hintergrundunabhängige Formulierung der Quantenfeldtheorie, die General Boundary Formulation, betrachtet. Die General Boundary Formulation wird dann auf den Unruh-Effekt angewendet und erste Versuche werden unternommen massive Materiefelder auf tensoriellen Raumzeiten zu quantisieren.

An investigation of information loss in black hole spacetimes is performed. We demon- strate that the definition of particles as energy levels of the Harmonic oscillator will not have physical significance in general and is thus not a good instrument to study the ra- diation of black holes. This is due to the ambiguity of the choice of coordinates on the phase space of the quantum field. We demonstrate how to identify quantum states in the functional Schr ̈dinger picture. o We demonstrate that information is truly lost in the case of a Vaidya black hole (a black hole formed from null dust) if we neglect back reaction. This is done by quantizing the constrained classical system of a Klein-Gordon field in a Vaidya background. The interaction picture of quantum mechanics can be applied to this system. We find a physically well motivated vacuum state for a spherically symmetric space- time with an extra conformal Killing vector. We also demonstrate how to calculate the response of a particle detector in the a LeMaitre-Tolman-Bondi spacetime with a self- similarity. Finally, some of the claims and confusion surrounding Unruh radiation, Hawking radiation and the equivalence principle are investigated and shown to be false.