A white dwarf is most likely the end stage of a low mass star like our Sun, which results when the parent star consumes all the hydrogen in its core, thus bringing fusion to a halt. It is a dense and compact object, where the inward gravitational pull is balanced by the outward pressure arising due to the motion of its constituent degenerate electrons. The theory of non-magnetized and non-rotating white dwarfs was formulated extensively by S. Chandrasekhar in the 1930s, who also proposed a maximum possible mass for this objects, known as the Chandrasekhar limit (Chandrasekhar 1935)1. White dwarfs are believed to be the progenitors of extremely bright explosions called type Ia supernovae (SNeIa). SNeIa are extremely important and popular astronomical events, which are hypothesized to be triggered in white dwarfs having mass close to the famous Chandrasekhar limit ∼ 1.44M⊙. The characteristic nature of the variation of luminosity with time of SNeIa is believed to be powered by the decay of 56Ni to 56Co and, finally, to 56Fe. This feature, along with the consistent mass of the exploding white dwarf, is deeply linked with their utilization as “standard candles” for cosmic distance measurement. In fact, SNeIa measurements were instrumental in establishing the accelerated nature of the current expansion of the universe (Perlmutter et al. 1999). However, several recently observed peculiar SNeIa do not conform to this traditional explanation. Some of these SNeIa are highly over-luminous, e.g. SN 2003fg, SN 2006gz, SN 2007if, SN 2009dc (Howell et al. 2006; Scalzo et al. 2010), and some others are highly under-luminous, e.g. SN 1991bg, SN 1997cn, SN 1998de, SN 1999by, SN 2005bl (Filippenko et al. 1992; Taubenberger et al. 2008). The luminosity of the former group of SNeIa implies a huge Ni-mass (often itself super-Chandrasekhar), invoking highly super-Chandrasekhar white dwarfs, having mass 2.1 − 2.8M⊙, as their most plausible progenitors (Howell et al. 2006; Scalzo et al. 2010). On the other hand, the latter group produces as low as ∼ 0.1M⊙ of Ni (Stritzinger et al. 2006), which rather seem to favor sub-Chandrasekhar explosion scenarios. In this thesis, as the title suggests, we have endeavored to establish the existence of exotic, super- and sub-Chandrasekhar limiting mass white dwarfs, in order to explain the aforementioned peculiar SNeIa. This is an extremely important puzzle to solve in order to comprehensively understand the phenomena of SNeIa, which in turn is essential for the correct interpretation of the evolutionary history of the universe. Effects of magnetic field: White dwarfs have been observed to be magnetized, having surface fields as high as 105 − 109 G (Vanlandingham et al. 2005). The interior field of a white dwarf cannot be probed directly but it is quite likely that it is several orders of magnitude higher than the surface field. The theory of weakly magnetized white dwarfs has been investigated by a few authors, however, their properties do not starkly contrast with that of the non-magnetized cases (Ostriker & Hartwick 1968). In our venture to find a fundamental basis behind the formation of super-Chandrasekhar white dwarfs, we have explored in this thesis the impact of stronger magnetic fields on the properties of white dwarfs, which has so far been overlooked. We have progressed from a simplistic to a more rigorous, self-consistent model, by adding complexities step by step, as follows: • spherically symmetric Newtonian model with constant (central) magnetic field • spherically symmetric general relativistic model with varying magnetic field • model with self-consistent departure from spherical symmetry by general relativis-tic magnetohydrodynamic (GRMHD) numerical modeling. We have started by exploiting the quantum mechanical effect of Landau quanti-zation due to a maximum allowed equipartition central field greater than a critical value Bc = 4.414 × 1013 G. To begin with, we have carried out the calculations in a Newtonian framework assuming spherically symmetric white dwarfs. The primary ef-fect of Landau quantization is to stiffen the equation of state (EoS) of the underlying electron degenerate matter in the high density regime, and, hence, yield significantly super-Chandrasekhar white dwarfs having mass much & 2M⊙ (Das & Mukhopadhyay 2012a,b). Consequently, we have proposed a new mass limit for magnetized white dwarfs which may establish the aforementioned peculiar, over-luminous SNeIa as new standard candles (Das & Mukhopadhyay 2013a,b). We have furthermore predicted possible evo-lutionary scenarios by which super-Chandrasekhar white dwarfs could form by accretion on to a commonly observed magnetized white dwarf, by invoking the phenomenon of flux freezing, subsequently ending in over-luminous, super-Chandrasekhar SNeIa (Das et al. 2013). Before moving on to a more complex model, we have justified the assumptions in our simplistic model, in the light of various related physics issues (Das & Mukhopad-hyay 2014b), and have also clarified, and, hence, removed some serious misconceptions regarding our work (Das & Mukhopadhyay 2015c). Next, we have considered a more self-consistent general relativistic framework. We have obtained stable solutions of magnetostatic equilibrium models for white dwarfs pertaining to various magnetic field profiles, however, still in spherical symmetry. We have showed that in this framework, a maximum stable mass as high as ∼ 3.3M⊙ can be realized (Das & Mukhopadhyay 2014a). However, it is likely that the anisotropic effect due to a strong magnetic field may cause a deformation in the spherical structure of the white dwarfs. Hence, in order to most self-consistently take into account this departure from spherical symmetry, we have constructed equilibrium models of strongly magnetized, static, white dwarfs in a general relativistic framework, first time in the literature to the best of our knowledge. In order to achieve this, we have modified the GRMHD code XNS (Pili et al. 2014), to apply it in the context of white dwarfs. Interestingly, we have found that signifi-cantly super-Chandrasekhar white dwarfs, in the range ∼ 1.7 − 3.4M⊙, are obtained for many possible field configurations, namely, poloidal, toroidal and mixed (Das & Mukhopadhyay 2015a). Furthermore, due to the inclusion of deformation caused by a strong magnetic field, super-Chandrasekhar white dwarfs are obtained for relatively lower central magnetic field strengths (∼ 1014 G) compared to that in the simplistic model — as correctly speculated in our first work of this series (Das & Mukhopadhyay 2012a). We have also found that although the characteristic deformation induced by a purely toroidal field is prolate, the overall shape remains quasi-spherical — justifying our earlier spherically symmetric assumption while constructing at least some models of strongly magnetized white dwarfs (Das & Mukhopadhyay 2014a). Indeed more accurate and extensive numerical analysis seems to have validated our analytical findings. Thus, very interestingly, our investigation has established that magnetized white dwarfs can indeed have mass that significantly exceeds the Chandrasekhar limit, irre-spective of the origin of the underlying magnetic effect — a discovery which is not only of theoretical importance, but also has a direct astrophysical implication in explaining the progenitors of the peculiar, over-luminous, super-Chandrasekhar SNeIa. Effects of modified Einstein’s gravity: A large array of models has been required to explain the peculiar, over- and under- luminous SNeIa. However, it is unlikely that nature would seek mutually antagonistic scenarios to exhibit sub-classes of apparently the same phenomena, i.e., triggering of thermonuclear explosions in white dwarfs. Hence, driven by the aim to establish a unification theory of SNeIa, we have invoked in the last part of this thesis a modification to Einstein’s theory of general relativity in white dwarfs. The validity of general relativity has been tested mainly in the weak field regime, for example, through laboratory experiments and solar system tests. However, the question remains, whether general relativity requires modification in the strong gravity regime, such as, the expanding universe, the region close to a black hole and neutron star. For instance, there is evidence from observational cosmology that the universe has undergone two epochs of cosmic acceleration, the theory behind which is not yet well understood. The period of acceleration in the early universe is known as inflation, while the current accelerated expansion is often explained by invoking a mysterious dark energy. An alternative approach to explain the mysteries of inflation and dark energy is to modify the underlying gravitational theory itself, as it conveniently avoids involving any exotic form of matter. Several modified gravity theories have been proposed which are extensions of Einstein’s theory of general relativity. A popular class of such theories is known as f (R) gravity (e.g. see de Felice & Tsujikawa 2010), where the Lagrangian density f of the gravitational field is an arbitrary function of the Ricci scalar R. In the context of astrophysical compact objects, so far, modified gravity theories have been applied only to neutron stars, which are much more compact than white dwarfs, in order to test the validity of such theories in the strong field regime (e.g. Cooney et al. 2010; Arapoˇglu et al. 2011). Moreover, a general relativistic correction itself does not seem to modify the properties of a white dwarf appreciably when compared to Newtonian calculations. Our venture of exploring modified gravity in white dwarfs in this thesis, is a first in the literature to the best of our knowledge. We have exploited the advantage that white dwarfs have over neutron stars, i.e., their EoS is well established. Hence, any change in the properties of white dwarfs can be solely attributed to the modification of the underlying gravity, unlike in neutron stars, where similar effects could be produced by invoking a different EoS. We have explored a popular, yet simple, model of f (R) gravity, known as the Starobinsky model (Starobinsky 1980) or R−squared model, which was originally pro-posed to explain inflation. Based on this model, we have first shown that modified gravity reproduces those results which are already explained in the paradigm of general relativity (and Newtonian framework), namely, low density white dwarfs in this context. This is a very important test of the modified gravity model and is furthermore necessary to constrain the underlying model parameter. Next, depending on the magnitude and sign of a single model parameter, we have not only obtained both highly super-Chandrasekhar and highly sub-Chandrasekhar limiting mass white dwarfs, but we have also established them as progenitors of the peculiar, over- and under-luminous SNeIa, respectively (Das & Mukhopadhyay 2015b). Thus, an effectively single underlying the-ory unifies the two apparently disjoint sub-classes of SNeIa, which have so far hugely puzzled astronomers. To summarize, in the first part of the thesis, we have established the enormous significance of magnetic fields in white dwarfs in revealing the existence of significantly super-Chandrasekhar white dwarfs. These super-Chandrasekhar white dwarfs could be ideal progenitors of the peculiar, over-luminous SNeIa, which can, hence, be used as new standard candles of cosmic distance measurements. In the latter part of the thesis, we have established the importance of a modified theory of Einstein’s gravity in revealing both highly super- and highly sub-Chandrasekhar limiting mass white dwarfs. We have furthermore demonstrated how such a theory can serve as a missing link between the peculiar, super- and sub-Chandrasekhar SNeIa. Thus, the significance of the current thesis lies in the fact that it not only questions the uniqueness of the Chandrasekhar mass-limit for white dwarfs, but it also argues for the need of a modified theory of Einstein’s gravity to explain astrophysical observations.

“Linguistic relativity” has been studied for a long time. Many empirical studies have been conducted on cross-linguistic differences to find support for the influence of language on thought. This study proposes viewpoint (defined as the point from which the conceptualizer sees and construes the event) as a cross-linguistic difference, and explores whether the linguistic constraint and preference of subjective/objective construal can affect one’s cognitive activity as viewpoint. As Japanese is a subjectivity-prominent language whereas Swedish is not, data elicited from monolingual adolescences (aged 12-16) in Japan and Sweden were compared. A set of tasks which consisted of non-verbal tasks (scene-visualisation) and verbal tasks (narrative of comic strips) was performed in order to elicit the participants’ viewpoints. The same set of tasks was assigned to simultaneous Swedish-Japanese bilingual adolescences in Sweden. The bilinguals took the set of non-verbal and verbal tasks twice, once in Swedish and once in Japanese. The results demonstrated a clear difference between the monolingual groups both in the non-verbal and verbal tasks. The Japanese monolinguals showed a higher preference for subjective viewpoint. The bilinguals’ viewpoint preference had a tendency to fall between that of monolinguals of both languages. This finding indicates that the bilinguals’ viewpoint preference may be influenced by both languages. This study demonstrates for the first time that the speaker’s viewpoint can be affected not only in verbal tasks but also in non-verbal tasks. The findings suggest that a language may influence the speaker’s way of construing events. It is also implied that the influences from different languages in bilinguals can be bidirectional. However, the influence does not seem to be all or nothing. Regardless of the language, one’s event construal is more or less the same. Nevertheless, the findings indicate that the linguistic subjectivity in a language tends to counteract the universal construal. / Språkrelativitet (Linguistic relativity) har studerats under lång tid. Många empiriska studier har studerat om och i så fall hur språk påverkar tänkandet och eventuella skillnader mellan olika språk. Denna studie föreslår perspektivpreferens för att beskriva ur vilket perspektiv en berättare återger skeenden. Studien utforskar om ett språks lingvistiska begränsningar och preferens för subjektiva/objektiva tolkningar av skeenden påverkar personers kognitiva aktivitet som val av perspektiv. Japanska är ett tydligt subjektivt framträdande språk medan svenskan inte är det. Därför jämfördes data från enspråkiga ungdomar (12-16 år gamla) i Japan och i Sverige. För att klarlägga deltagarnas perspektivpreferens genomfördes två delstudier, dels en icke-verbal studie (en scenvisualisering) och dels en verbal studie (ett återberättande av tecknade serier). Samma delstudier genomfördes också till simultant svensk-japanska tvåspråkiga ungdomar i Sverige. De tvåspråkiga deltagarna gjorde de verbala och icke-verbala delstudierna i två omgångar, en gång på svenska och en gång på japanska. Resultatet visade en klar skillnad mellan de enspråkiga grupperna, både i den icke-verbala och verbala delstudien. De japanska enspråkiga deltagarna visade högre preferens för subjektiva tolkningar. De tvåspråkiga deltagarnas perspektivpreferens hade en tendens att komma mellan de enspråkiga deltagarnas preferenser. Detta indikerar att de tvåspråkigas val av perspektiv påverkades av deras tvåspråkighet. Studien visar för första gången att berättarens val av perspektiv kan påverkas inte bara i verbala uppgifter utan också i icke-verbala uppgifter. Resultaten från studien indikerar att ett språk kan påverka en berättares sätt att tolka händelser, och att påverkan från de olika språken hos tvåspråkiga kan vara dubbelriktad. Oberoende av språk återges skeenden på ett likartat sätt. Studien indikerar emellertid att lingvistisk subjektivitet i ett språk tenderar att motverka ett universellt återgivande av perspektiv.

Nous étudions l’analyse asymptotique en relativité générale sous deux aspects: le peeling et le scattering (diffusion) conforme. Le peeling est construit pour les champs scalaires linéaire et non-linéaires et pour les champs de Dirac en espace-temps de Kerr (qui est non-stationnaire et à symétrie simplement axiale), généralisant les travaux de L. Mason et J-P. Nicolas (2009, 2012). La méthode des champs de vecteurs (estimations d’énergie géométriques) et la technique de compactification conforme sont développées. Elles nous permettent de formuler les définitions du peeling à tous ordres et d’obtenir les données initiales optimales qui assurent ces comportements. Une théorie de la diffusion conforme pour les équations de champs sans masse de spîn n/2 dans l’espace-temps de Minkowski est construite.En effectuant les compactifications conformes (complète et partielle), l’espace-temps est complété en ajoutant une frontière constituée de deux hypersurfaces isotropes représentant respectivement les points limites passés et futurs des géodésiques de type lumière. Le comportement asymptotique des champs s’obtient en résolvant le problème de Cauchy pour l’équation rééchelonnée et en considérant les traces des solutions sur ces bords. L’inversibilité des opérateurs de trace, qui associent le comportement asymptotique passé ou futur aux données initiales, s’obtient en résolvant le problème de Goursat sur le bord conforme. L’opérateur de diffusion conforme est alors obtenu par composition de l’opérateur de trace futur avec l’inverse de l’opérateur de trace passé. / This work explores two aspects of asymptotic analysis in general relativity: peeling and conformal scattering.On the one hand, the peeling is constructed for linear and nonlinear scalar fields as well as Dirac fields on Kerr spacetime, which is non-stationary and merely axially symmetric. This generalizes the work of L. Mason and J-P. Nicolas (2009, 2012). The vector field method (geometric energy estimates) and the conformal technique are developed. They allow us to formulate the definition of the peeling at all orders and to obtain the optimal space of initial data which guarantees these behaviours. On the other hand, a conformal scattering theory for the spin-n/2 zero rest-mass equations on Minkowski spacetime is constructed. Using the conformal compactifications (full and partial), the spacetime is completed with two null hypersurfaces representing respectively the past and future end points of null geodesics. The asymptotic behaviour of fields is then obtained by solving the Cauchy problem for the rescaled equation and considering the traces of the solutions on these hypersurfaces. The invertibility of the trace operators, that to the initial data associate the future or past asymptotic behaviours, is obtained by solving the Goursat problem on the conformal boundary. The conformal scattering operator is then obtained by composing the future trace operator with the inverse of the past trace operator.

In the review part of the thesis we summarize various modified theories of gravity, especially those that are characterized by additional curvature invariants in the Lagrangian density. Further, we review non-twisting geometries, especially their Kundt subclass. Finally, from the principle of least action we derive field equations for the case with the Lagrangian density corresponding to an arbitrary function of the curvature invariants. In the original part of the thesis we explicitly express particular components of the field equations for non-gyratonic Kundt geometry in generic quadratic gravity in arbitrary dimension. Then we discuss how this, in general fourth order, field equations restrict the Kundt metric in selected geome- trically privileged situations. We also analyse the special case of Gauss-Bonnet theory. 1

Le problème des singularités en relativité générale remonte à la première solution exacte de la théorie obtenue en 1915, à savoir celle du trou noir de Schwarzschild. Qu'elles soient de coordonnée ou de courbure, ces singularités ont longtemps questionné les physiciens qui parvinrent à mieux les caractériser à la fin des années 1960. Cela conduisit aux fameux théorèmes sur les singularités, s'appliquant à la fois aux trous noirs et en cosmologie, basés sur un comportement classique du contenu en matière de l'espace-temps résumé par des conditions d'énergie. La violation de ces conditions dans les processus quantiques pourrait indiquer que les singularités doivent être vues comme des limitations de la relativité générale, pouvant ainsi disparaître dans une théorie plus générale de la gravité quantique.Dans l'attente d'une telle théorie, nous avons pour objectif dans cette thèse d'étudier les espaces-temps de trous noirs dépourvus de toute singularité ainsi que leurs conséquences observationnelles. A cette fin, nous considérons à la fois des modifications de la relativité générale et le couplage de la théorie à des contenus en matière exotiques. Dans le premier cas nous montrons qu'il est possible de retrouver des trous noirs réguliers à symétrie sphérique connus, tout d'abord en principe avec la théorie tenseur-scalaire de gravité mimétique, puis implicitement par le biais d'une déformation de la contrainte hamiltonienne en relativité générale inspirée des techniques de gravitation quantique à boucles. Dans le second cas nous restons dans le cadre de la relativité générale, et considérons des tenseurs énergie-impulsion effectifs. Ils sont en premier lieu associés à un modèle régulier à la Hayward en rotation fournissant dans un certain régime un premier exemple de trou noir en rotation exempt de toute singularité, puis à un espace-temps dynamique décrivant la formation et l'évaporation d'un trou noir sans singularité. Pour ce dernier, nous montrons que tout modèle basé sur l'effondrement gravitationnel de coquilles de genre lumière visant à décrire l'évaporation de Hawking est voué à violer les conditions sur l'énergie dans une région non compacte de l'espace-temps. Enfin, l'étude théorique de la métrique de Hayward en rotation est accompagnée de simulations numériques d'un tel objet au centre de la Voie Lactée, obtenues à l'aide du code de calcul de trajectoires de particules Gyoto en reproduisant les propriétés connues de la structure d'accrétion du trou noir présumé Sgr A*. Ces simulations permettent d'illustrer deux régimes très différents de la métrique, avec ou sans horizon, et soulignent la difficulté d'affirmer avec certitude la présence d'un horizon à partir d'images en champ fort telles que celles obtenues par l'instrument Event Horizon Telescope. / The issue of singularities in General Relativity dates back to the very first solution to the equations of the theory, namely Schwarzschild's 1915 black hole. Whether they be of coordinate or curvature nature, these singularities have long puzzled physicists, who managed to better characterize them in the late 60's. This led to the famous singularity theorems applying both to cosmology and black holes, and which assume a classical behaviour of the matter content of spacetime summarized in the so-called energy conditions. The violation of these conditions by quantum phenomena supports the idea that singularities are to be seen as a limitation of General Relativity, and would be cured in a more general theory of quantum gravity. In this thesis, pending for such a theory, we aim at investigating black hole spacetimes deprived of any singularity as well as their observational consequences. To that purpose, we consider both modifications of General Relativity and the coupling of Einstein's theory to exotic matter contents. In the first case, we show that one can recover the static spherically symmetric non-singular black holes of Bardeen and Hayward in principle in mimetic gravity, and implicitly by a deformation of General Relativity's hamiltonian constraint in an approach based on loop quantum gravity techniques. In the second case, we stay inside the framework of General Relativity and consider effective energy-momentum tensors associated with a fully regular rotating Hayward metric and with a dynamical spacetime describing the formation and evaporation of a non-singular black hole. For the latter, we show that all models based on the collapse of ingoing null shells and willing to describe Hawking’s evaporation are doomed to violate the energy conditions in a non-compact region of spacetime. Lastly, the theoretical study of the rotating Hayward metric comes with numerical simulations of such an object at the center of the Milky Way, using the ray-tracing code Gyoto and mimicking the known properties of the accretion structure of Sgr A*. These simulations allow exhibiting the two very different regimes of the metric, with or without horizon, and emphasize the difficulty of asserting the presence of a horizon from strong-field images as the ones provided by the Event Horizon Telescope.

L'existence de la masse négative a un sens parfaitement physique du moment que les conditions d'énergie dominante sont satisfaites par le tenseur énergie-impulsion correspondant. Jusqu'à maintenant, seules des configurations de masses négatives avaient été trouvées. On démontre l'existence de bulles de masse négative stables dans un espace-temps qui s'approche asymptotiquement d'un espace-temps de de Sitter. Les bulles sont des solutions aux équations d'Einstein qui correspondent à une région intérieure qui contient une distribution de masse spécifique séparée par une coquille mince de l'espace-temps à masse négative de Schwarzschild-de Sitter à l'extérieur. Ensuite, on applique les conditions de jonction d'Israel à la frontière de la bulle ce qui impose la conservation d'énergie-impulsion à travers la surface. Les conditions de jonction donnent une équation pour un potentiel pour le rayon de la bulle qui dépend de la distribution de masse à l'intérieur, ou vice versa. Finalement, on trouve un potentiel qui aboutit à une solution stable, statique et non-singulière, ce qui crée une distribution de masse interne qui satisfait les conditions d'énergie dominante partout à l'intérieur. Cependant, la bulle ne satisfait pas ces conditions. De plus, on trouve une solution stable, statique et non-singulière pour une géométrie interne de de Sitter pure. La solution est fondamentalement différente: elle requiert que la densité d'énergie de la bulle change avec le rayon. La condition d'énergie dominante est satisfaite partout. / Negative mass makes perfect physical sense as long as the dominant energy condition is satisfied by the corresponding energy-momentum tensor. Until now, only configurations of negative mass have been found. We demonstrate the existence of stable, negative-mass bubbles in an asymptotic de Sitter space-time. The bubbles are solutions of the Einstein equations which correspond to an interior region of space-time containing a specific distribution of mass separated by a thin wall from the exact, negative mass Schwarzschild-de Sitter space-time in the exterior. Then, we apply the Israel junction conditions at the wall which impose the conservation of energy and momentum across the wall. The junction conditions give rise to an effective potential for the radius of the wall that depends on the interior mass distribution, or vice versa. Finally, we find a potential that gives rise to stable, non-singular, static solutions, which yields an interior mass distribution that everywhere satisfies the dominant energy condition. However, the energy momentum of the wall does not satisfy the dominant energy condition. Moreover, we find a stable, non-singular, static solution for a pure de Sitter geometry inside the bubble. The solution is fundamentally different: the energy density of the bubble is no longer a constant, but now varies with the radius. The dominant energy condition is everywhere satisfied.

Albert Einstein published the English translation of Relativity: The Special and General Theory in the midst of two big events in 1920: the confirmation of the two theories of relativity and spacetime in 1919 and the Nobel prize in physics in 1921. The new global celebrity wanted to make the theories intelligible and readable for an international English-speaking audience, an audience that also included antagonistic scientists and even anti-Semites. The aim of this thesis is to do a rhetorical analysis of Einstein’s character, his ethos, in Relativity, with a specific focus on creation of credibility in regard to his historical context: scientific ideals, values and norms as well as the political and cultural tendencies in Europe during the early 20th century. This was done firstly by identifying the implied auditor. Secondly, based on the material, I have identified three stereotypes or characters – the professional idealist, the mentor and the internationalist –  which emphases different features and capacities that are crucial for the credibility of the text. Thirdly, by using these stereotypes and in regard to the specific historical context, I investigated how Einstein developed his primary ethos into a secondary ethos in the text. The rhetorical analysis of Einstein’s Relativity shows that his ethos stands in relation to the social and cultural perception of the virtuous epistemic scientist; to fight prejudices regarding being a Jewish-German theoretical physicist; and, noteworthy, a way to produce a well-needed international space – a crucial alternative to continue the positivistic knowledge production counter to the nationalistic project.

<p>This dissertation is concerned with two of the largest questions that we can ask about the nature of physical reality: first, whether physical reality begin to exist and, second, what criteria would physical reality have to fulfill in order to have had a beginning? Philosophers of religion and theologians have previously addressed whether physical reality began to exist in the context of defending the Kal{\'a}m Cosmological Argument (KCA) for theism, that is, (P1) everything that begins to exist has a cause for its beginning to exist, (P2) physical reality began to exist, and, therefore, (C) physical reality has a cause for its beginning to exist. While the KCA has traditionally been used to argue for God's existence, the KCA does not mention God, has been rejected by historically significant Christian theologians such as Thomas Aquinas, and raises perennial philosophical questions -- about the nature and history of physical reality, the nature of time, the nature of causation, and so on -- that should be of interest to all philosophers and, perhaps, all humans. While I am not a religious person, I am interested in the questions raised by the KCA. In this dissertation, I articulate three necessary conditions that physical reality would need to fulfill in order to have had a beginning and argue that, given the current state of philosophical and scientific inquiry, we cannot determine whether physical reality began to exist.</p>

In this work the extension of the criterion for local thermal equilibrium by Buchholz, Ojima and Roos to curved spacetime as introduced by Schlemmer is investigated. Several problems are identified and especially the instability under time evolution which was already observed by Schlemmer is inspected. An alternative approach to local thermal equilibrium in quantum field theories on curved spacetimes is presented and discussed. In the following the dynamic system of the linear field and matter perturbations in the generic model of inflation is studied in the view of ambiguity of quantisation. In the last part the compatibility of the temperature fluctuations of the cosmic microwave background radiation with local thermal equilibrium is investigated.:1. Introduction 5 2. Technical Background 10 2.1. The Free Scalar Field on a Globally Hyperbolic Spacetime . . . . . . 10 2.1.1. Construction of the Scalar Field . . . . . . . . . . . . . . . . . 10 2.1.2. Algebra of Wick Products . . . . . . . . . . . . . . . . . . . . 13 2.1.3. Local Covariance Principle . . . . . . . . . . . . . . . . . . . . 17 2.2. Local Thermal Equilibirum . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.1. Global Thermodynamic Equilibrium - KMS States . . . . . . 21 2.2.2. Local Thermal Observables . . . . . . . . . . . . . . . . . . . 24 2.2.3. LTE on Flat Spacetime . . . . . . . . . . . . . . . . . . . . . . 29 2.2.4. LTE in Cosmological Spacetimes . . . . . . . . . . . . . . . . 32 2.3. Linear Scalar Cosmological Perturbations . . . . . . . . . . . . . . . . 34 2.3.1. Robertson-Walker Cosmology . . . . . . . . . . . . . . . . . . 35 2.3.2. Mathematical Background . . . . . . . . . . . . . . . . . . . . 38 2.3.3. Technical Framework and Formulae . . . . . . . . . . . . . . . 40 2.3.4. The Boltzmann Equation . . . . . . . . . . . . . . . . . . . . 46 2.3.5. The Sachs-Wolfe Effect for Adiabatic Perturbations . . . . . . 49 3. Towards a Refinement of the LTE Condition on Curved Spacetimes 54 3.1. Non-Minimal Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.1.1. Commutator Distribution . . . . . . . . . . . . . . . . . . . . 55 3.1.2. KMS Two-Point Function . . . . . . . . . . . . . . . . . . . . 57 3.1.3. Balanced Derivatives . . . . . . . . . . . . . . . . . . . . . . . 61 3.2. Conformally Static Spacetimes . . . . . . . . . . . . . . . . . . . . . . 65 3.2.1. Conformal KMS States . . . . . . . . . . . . . . . . . . . . . . 66 3.2.2. Extrinsic LTE in de Sitter Spacetime . . . . . . . . . . . . . . 71 3.3. Massive Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.3.1. Properties of the Model . . . . . . . . . . . . . . . . . . . . . 78 3.3.2. Bogoliubov Transformation . . . . . . . . . . . . . . . . . . . 80 3.3.3. Thermal Observables . . . . . . . . . . . . . . . . . . . . . . . 82 3.4. Towards an Alternative Concept . . . . . . . . . . . . . . . . . . . . . 91 3.4.1. Problems and Open Questions Concerning LTE . . . . . . . . 92 3.4.2. Dynamic Equations . . . . . . . . . . . . . . . . . . . . . . . . 94 3.4.3. Positivity Inequalities . . . . . . . . . . . . . . . . . . . . . . . 96 3.4.4. Macroobservable Interpretation . . . . . . . . . . . . . . . . . 100 3.5. An Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4. Cosmological Perturbation Theory 105 4.1. Dynamics of Perturbations in Inflation . . . . . . . . . . . . . . . . . 106 4.1.1. CCR Quantisation is Ambiguous . . . . . . . . . . . . . . . . 106 4.1.2. Canonical Symplectic Form . . . . . . . . . . . . . . . . . . . 111 4.1.3. The Algebraic Point of View . . . . . . . . . . . . . . . . . . . 117 4.2. LTE States in Cosmology . . . . . . . . . . . . . . . . . . . . . . . . 120 4.2.1. The Link to Fluid Dynamics . . . . . . . . . . . . . . . . . . . 120 4.2.2. Incompatibility of LTE with Sachs-Wolfe Effect . . . . . . . . 125 5. Conclusion and Outlook 131 A. Technical proofs 136 A.1. Proof of Lemma 3.2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 A.2. Proof of Lemma 3.2.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 A.3. Proof of Lemma 3.4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 A.4. Idea of Proof for Conjecture 3.4.3 . . . . . . . . . . . . . . . . . . . . 144 B. Introduction to Probability Theory 146 Bibliography 150 Correction of Lemma 3.1.2 155 / In dieser Arbeit wird die von Schlemmer eingeführte Erweiterung des Kriteriums für lokales thermisches Gleichgewicht in Quantenfeldtheorien von Buchholz, Ojima und Roos auf gekrümmte Raumzeiten untersucht. Dabei werden verschiedene Probleme identifiziert und insbesondere die bereits von Schlemmer gezeigte Instabilität unter Zeitentwicklung untersucht. Es wird eine alternative Herangehensweise an lokales thermisches Gleichgewicht in Quantenfeldtheorien auf gekrümmten Raumzeiten vorgestellt und deren Probleme diskutiert. Es wird dann eine Untersuchung des dynamischen Systems der linearen Feld- und Metrikstörungen im üblichen Inflationsmodell mit Blick auf Uneindeutigkeit der Quantisierung durchgeführt. Zuletzt werden die Temperaturfluktuationen der kosmischen Hintergrundstrahlung auf Kompatibilität mit lokalem thermalem Gleichgewicht überprüft.:1. Introduction 5 2. Technical Background 10 2.1. The Free Scalar Field on a Globally Hyperbolic Spacetime . . . . . . 10 2.1.1. Construction of the Scalar Field . . . . . . . . . . . . . . . . . 10 2.1.2. Algebra of Wick Products . . . . . . . . . . . . . . . . . . . . 13 2.1.3. Local Covariance Principle . . . . . . . . . . . . . . . . . . . . 17 2.2. Local Thermal Equilibirum . . . . . . . . . . . . . . . . . . . . . . . 21 2.2.1. Global Thermodynamic Equilibrium - KMS States . . . . . . 21 2.2.2. Local Thermal Observables . . . . . . . . . . . . . . . . . . . 24 2.2.3. LTE on Flat Spacetime . . . . . . . . . . . . . . . . . . . . . . 29 2.2.4. LTE in Cosmological Spacetimes . . . . . . . . . . . . . . . . 32 2.3. Linear Scalar Cosmological Perturbations . . . . . . . . . . . . . . . . 34 2.3.1. Robertson-Walker Cosmology . . . . . . . . . . . . . . . . . . 35 2.3.2. Mathematical Background . . . . . . . . . . . . . . . . . . . . 38 2.3.3. Technical Framework and Formulae . . . . . . . . . . . . . . . 40 2.3.4. The Boltzmann Equation . . . . . . . . . . . . . . . . . . . . 46 2.3.5. The Sachs-Wolfe Effect for Adiabatic Perturbations . . . . . . 49 3. Towards a Refinement of the LTE Condition on Curved Spacetimes 54 3.1. Non-Minimal Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.1.1. Commutator Distribution . . . . . . . . . . . . . . . . . . . . 55 3.1.2. KMS Two-Point Function . . . . . . . . . . . . . . . . . . . . 57 3.1.3. Balanced Derivatives . . . . . . . . . . . . . . . . . . . . . . . 61 3.2. Conformally Static Spacetimes . . . . . . . . . . . . . . . . . . . . . . 65 3.2.1. Conformal KMS States . . . . . . . . . . . . . . . . . . . . . . 66 3.2.2. Extrinsic LTE in de Sitter Spacetime . . . . . . . . . . . . . . 71 3.3. Massive Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 3.3.1. Properties of the Model . . . . . . . . . . . . . . . . . . . . . 78 3.3.2. Bogoliubov Transformation . . . . . . . . . . . . . . . . . . . 80 3.3.3. Thermal Observables . . . . . . . . . . . . . . . . . . . . . . . 82 3.4. Towards an Alternative Concept . . . . . . . . . . . . . . . . . . . . . 91 3.4.1. Problems and Open Questions Concerning LTE . . . . . . . . 92 3.4.2. Dynamic Equations . . . . . . . . . . . . . . . . . . . . . . . . 94 3.4.3. Positivity Inequalities . . . . . . . . . . . . . . . . . . . . . . . 96 3.4.4. Macroobservable Interpretation . . . . . . . . . . . . . . . . . 100 3.5. An Application . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 4. Cosmological Perturbation Theory 105 4.1. Dynamics of Perturbations in Inflation . . . . . . . . . . . . . . . . . 106 4.1.1. CCR Quantisation is Ambiguous . . . . . . . . . . . . . . . . 106 4.1.2. Canonical Symplectic Form . . . . . . . . . . . . . . . . . . . 111 4.1.3. The Algebraic Point of View . . . . . . . . . . . . . . . . . . . 117 4.2. LTE States in Cosmology . . . . . . . . . . . . . . . . . . . . . . . . 120 4.2.1. The Link to Fluid Dynamics . . . . . . . . . . . . . . . . . . . 120 4.2.2. Incompatibility of LTE with Sachs-Wolfe Effect . . . . . . . . 125 5. Conclusion and Outlook 131 A. Technical proofs 136 A.1. Proof of Lemma 3.2.5 . . . . . . . . . . . . . . . . . . . . . . . . . . . 136 A.2. Proof of Lemma 3.2.6 . . . . . . . . . . . . . . . . . . . . . . . . . . . 138 A.3. Proof of Lemma 3.4.2 . . . . . . . . . . . . . . . . . . . . . . . . . . . 141 A.4. Idea of Proof for Conjecture 3.4.3 . . . . . . . . . . . . . . . . . . . . 144 B. Introduction to Probability Theory 146 Bibliography 150 Correction of Lemma 3.1.2 155

The discovery of topological quantum states of matter has required physicists to look beyond Landau’s theory of symmetry-breaking, previously the main paradigm for<br>studying states of matter. This has led also to the development of new topological theories for describing the novel properties. In this dissertation an investigation in this<br>frontier research area is presented, which looks at the interplay between the quantum geometry of these states, defects and disorder. After a brief introduction to the topological quantum states of matter considered herein, some aspects of my work in this area are described. First, the disorder-induced band structure engineering of topological insulator surface states is considered, which is possible due to their resilience from Anderson localization, and believed to be a consequence of their topological origin.<br>Next, the idiosyncratic behavior of these same surface states is considered, as observed in experiments on thin film topological insulators, in response to competition between<br>hybridization effects and an in-plane magnetic field. Then moving in a very different direction, the uncovering of topological ‘gravitational’ response is explained: the<br>topologically-protected charge response of two dimensional gapped electronic topological states to a special kind of 0-dimensional boundary – a disclination – that encodes spatial curvature. Finally, an intriguing relation between the gravitational response of quantum Hall states, and their response to an apparently unrelated perturbation – nonuniform electric fields is reported. <br>