Sostanzialismo e relazionalismo dello spaziotempo alla luce della relatività generale

Until recently the debate on the ontology of spacetime had only a philosophical significance, since, from a physical point of view, General Relativity has been made "immune" to the consequences of the "Hole Argument" simply by reducing the subject to the assertion that solutions of Einstein equations which are mathematically different and related by an active diffeomorfism are physically equivalent. From a technical point of view, the natural reading of the consequences of the "Hole Argument” has always been to go further and say that the mathematical representation of spacetime in General Relativity inevitably contains a “superfluous structure” brought to light by the gauge freedom of the theory. This position of apparent split between the philosophical outcome and the physical one has been corrected thanks to a meticulous and complicated formal analysis of the theory in a fundamental and recent (2006) work by Luca Lusanna and Massimo Pauri entitled “Explaining Leibniz equivalence as difference of non-inertial appearances: dis-solution of the Hole Argument and physical individuation of point-events”. The main result of this article is that of having shown how, from a physical point of view, point-events of Einstein empty spacetime, in a particular class of models considered by them, are literally identifiable with the autonomous degrees of freedom of the gravitational field (the Dirac observables, DO). In the light of philosophical considerations based on realism assumptions of the theories and entities, the two authors then conclude by saying that spacetime point-events have a degree of "weak objectivity", since they, depending on a NIF (non-inertial frame), unlike the points of the homogeneous newtonian space, are plunged in a rich and complex non-local holistic structure provided by the “ontic part” of the metric field. Therefore according to the complex structure of spacetime that General Relativity highlights and within the declared limits of a methodology based on a Galilean scientific representation, we can certainly assert that spacetime has got "elements of reality", but the inevitably relational elements that are in the physical detection of point-events in the vacuum of matter (highlighted by the “ontic part” of the metric field, the DO) are closely dependent on the choice of the global spatiotemporal laboratory where the dynamics is expressed (NIF). According to the two authors, a peculiar kind of structuralism takes shape: the point structuralism, with common features both of the absolutist and substantival tradition and of the relationalist one. The intention of this thesis is that of proposing a method of approaching the problem that is, at least at the beginning, independent from the previous ones, that is to propose an approach based on the possibility of describing the gravitational field at three distinct levels. In other words, keeping the results achieved by the work of Lusanna and Pauri in mind and following their underlying philosophical assumptions, we intend to partially converge to their structuralist approach, but starting from what we believe is the "foundational peculiarity" of General Relativity, which is that characteristic inherent in the elements that constitute its formal structure: its essentially geometric nature as a theory considered regardless of the empirical necessity of the measure theory. Observing the theory of General Relativity from this perspective, we can find a "triple modality" for describing the gravitational field that is essentially based on a geometric interpretation of the spacetime structure. The gravitational field is now "visible" no longer in terms of its autonomous degrees of freedom (the DO), which, in fact, do not have a tensorial and, therefore, nor geometric nature, but it is analyzable through three levels: a first one, called the potential level (which the theory identifies with the components of the metric tensor), a second one, known as the connections level (which in the theory determine the forces acting on the mass and, as such, offer a level of description related to the one that the newtonian gravitation provides in terms of components of the gravitational field) and, finally, a third level, that of the Riemann tensor, which is peculiar to General Relativity only. Focusing from the beginning on what is called the "third level" seems to present immediately a first advantage: to lead directly to a description of spacetime properties in terms of gauge-invariant quantites, which allows to "short circuit" the long path that, in the treatises analyzed, leads to identify the "ontic part” of the metric field. It is then shown how to this last level it is possible to establish a “primitive level of objectivity” of spacetime in terms of the effects that matter exercises in extended domains of spacetime geometrical structure; these effects are described by invariants of the Riemann tensor, in particular of its irreducible part: the Weyl tensor. The convergence towards the affirmation by Lusanna and Pauri that the existence of a holistic, non-local and relational structure from which the properties quantitatively identified of point-events depend (in addition to their own intrinsic detection), even if it is obtained from different considerations, is realized, in our opinion, in the assignment of a crucial role to the degree of curvature of spacetime that is defined by the Weyl tensor even in the case of empty spacetimes (as in the analysis conducted by Lusanna and Pauri). In the end, matter, regarded as the physical counterpart of spacetime curvature, whose expression is the Weyl tensor, changes the value of this tensor even in spacetimes without matter. In this way, going back to the approach of Lusanna and Pauri, it affects the DOs evolution and, consequently, the physical identification of point-events (as our authors claim). In conclusion, we think that it is possible to see the holistic, relational, and non-local structure of spacetime also through the "behavior" of the Weyl tensor in terms of the Riemann tensor. This "behavior" that leads to geometrical effects of curvature is characterized from the beginning by the fact that it concerns extensive domains of the manifold (although it should be pointed out that the values of the Weyl tensor change from point to point) by virtue of the fact that the action of matter elsewhere indefinitely acts. Finally, we think that the characteristic relationality of spacetime structure should be identified in this "primitive level of organization" of spacetime.

Von nichtkommutativen Geometrien, ihren Symmetrien und etwas Hochenergiephysik

In den letzten fünf Jahren hat sich mit dem Begriff desspektralen Tripels eine Möglichkeit zur Beschreibungdes an Spinoren gekoppelten Gravitationsfeldes auf(euklidischen) nichtkommutativen Räumen etabliert. Die Dynamik dieses Gravitationsfeldes ist dabei durch diesogenannte spektrale Wirkung, dieSpur einer geeigneten Funktion des Dirac-Operators,bestimmt. Erstaunlicherweise kann man die vollständige Lagrange-Dichtedes (an das Gravitationsfeld gekoppelten) Standardmodellsder Elementarteilchenphysik, also insbesondere auch denmassegebenden Higgs-Sektor, als spektrale Wirkungeines entsprechenden spektralen Tripels ableiten. Diesesspektrale Tripel ist als Produkt des spektralenTripels der (kommutativen) Raumzeit mit einem speziellendiskreten spektralen Tripel gegeben. In der Arbeitwerden solche diskreten spektralen Tripel, die bis vorKurzem neben dem nichtkommutativen Torus die einzigen,bekannten nichtkommutativen Beispiele waren, klassifiziert. Damit kannnun auch untersucht werden, inwiefern sich dasStandardmodell durch diese Eigenschaft gegenüber anderenYang-Mills-Higgs-Theorien auszeichnet. Es zeigt sichallerdings, dasses - trotz mancher Einschränkung - eine sehr große Zahl vonModellen gibt, die mit Hilfe von spektralen Tripelnabgeleitet werden können. Es wäre aber auch denkbar, dass sich das spektrale Tripeldes Standardmodells durch zusätzliche Strukturen,zum Beispiel durch eine darauf ``isometrisch'' wirkendeHopf-Algebra, auszeichnet. In der Arbeit werden, um dieseFrage untersuchen zu können, sogenannte H-symmetrischespektrale Tripel, welche solche Hopf-Isometrien aufweisen,definiert.Dabei ergibt sich auch eine Möglichkeit, neue(H-symmetrische) spektrale Tripel mit Hilfe ihrerzusätzlichen Symmetrienzu konstruieren. Dieser Algorithmus wird an den Beispielender kommutativen Sphäre, deren Spin-Geometrie hier zumersten Mal vollständig in der globalen, algebraischen Sprache der NichtkommutativenGeometrie beschrieben wird, sowie dem nichtkommutativenTorus illustriert.Als Anwendung werden einige neue Beipiele konstruiert. Eswird gezeigt, dass sich für Yang-Mills Higgs-Theorien, diemit Hilfe von H-symmetrischen spektralen Tripeln abgeleitetwerden, aus den zusätzlichen Isometrien Einschränkungen andiefermionischen Massenmatrizen ergeben. Im letzten Abschnitt der Arbeit wird kurz auf dieQuantisierung der spektralen Wirkung für diskrete spektraleTripel eingegangen.Außerdem wird mit dem Begriff des spektralen Quadrupels einKonzept für die nichtkommutative Verallgemeinerungvon lorentzschen Spin-Mannigfaltigkeiten vorgestellt.

Development of muliplexed analytical methods based on bioluminescent whole-cell biosensors

The subject of this Ph.D. research thesis is the development and application of multiplexed analytical methods based on bioluminescent whole-cell biosensors. One of the main goals of analytical chemistry is multianalyte testing in which two or more analytes are measured simultaneously in a single assay. The advantages of multianalyte testing are work simplification, high throughput, and reduction in the overall cost per test. The availability of multiplexed portable analytical systems is of particular interest for on-field analysis of clinical, environmental or food samples as well as for the drug discovery process. To allow highly sensitive and selective analysis, these devices should combine biospecific molecular recognition with ultrasensitive detection systems. To address the current need for rapid, highly sensitive and inexpensive devices for obtaining more data from each sample,genetically engineered whole-cell biosensors as biospecific recognition element were combined with ultrasensitive bioluminescence detection techniques. Genetically engineered cell-based sensing systems were obtained by introducing into bacterial, yeast or mammalian cells a vector expressing a reporter protein whose expression is controlled by regulatory proteins and promoter sequences. The regulatory protein is able to recognize the presence of the analyte (e.g., compounds with hormone-like activity, heavy metals…) and to consequently activate the expression of the reporter protein that can be readily measured and directly related to the analyte bioavailable concentration in the sample. Bioluminescence represents the ideal detection principle for miniaturized analytical devices and multiplexed assays thanks to high detectability in small sample volumes allowing an accurate signal localization and quantification. In the first chapter of this dissertation is discussed the obtainment of improved bioluminescent proteins emitting at different wavelenghts, in term of increased thermostability, enhanced emission decay kinetic and spectral resolution. The second chapter is mainly focused on the use of these proteins in the development of whole-cell based assay with improved analytical performance. In particular since the main drawback of whole-cell biosensors is the high variability of their analyte specific response mainly caused by variations in cell viability due to aspecific effects of the sample’s matrix, an additional bioluminescent reporter has been introduced to correct the analytical response thus increasing the robustness of the bioassays. The feasibility of using a combination of two or more bioluminescent proteins for obtaining biosensors with internal signal correction or for the simultaneous detection of multiple analytes has been demonstrated by developing a dual reporter yeast based biosensor for androgenic activity measurement and a triple reporter mammalian cell-based biosensor for the simultaneous monitoring of two CYP450 enzymes activation, involved in cholesterol degradation, with the use of two spectrally resolved intracellular luciferases and a secreted luciferase as a control for cells viability. In the third chapter is presented the development of a portable multianalyte detection system. In order to develop a portable system that can be used also outside the laboratory environment even by non skilled personnel, cells have been immobilized into a new biocompatible and transparent polymeric matrix within a modified clear bottom black 384 -well microtiter plate to obtain a bioluminescent cell array. The cell array was placed in contact with a portable charge-coupled device (CCD) light sensor able to localize and quantify the luminescent signal produced by different bioluminescent whole-cell biosensors. This multiplexed biosensing platform containing whole-cell biosensors was successfully used to measure the overall toxicity of a given sample as well as to obtain dose response curves for heavy metals and to detect hormonal activity in clinical samples (PCT/IB2010/050625: “Portable device based on immobilized cells for the detection of analytes.” Michelini E, Roda A, Dolci LS, Mezzanotte L, Cevenini L , 2010). At the end of the dissertation some future development steps are also discussed in order to develop a point of care (POCT) device that combine portability, minimum sample pre-treatment and highly sensitive multiplexed assays in a short assay time. In this POCT perspective, field-flow fractionation (FFF) techniques, in particular gravitational variant (GrFFF) that exploit the earth gravitational field to structure the separation, have been investigated for cells fractionation, characterization and isolation. Thanks to the simplicity of its equipment, amenable to miniaturization, the GrFFF techniques appears to be particularly suited for its implementation in POCT devices and may be used as pre-analytical integrated module to be applied directly to drive target analytes of raw samples to the modules where biospecifc recognition reactions based on ultrasensitive bioluminescence detection occurs, providing an increase in overall analytical output.

Centrifuge modeling of earth-reinforced retaining walls

Object of this thesis has been centrifuge modelling of earth reinforced retaining walls with modular blocks facing in order to investigate on the influence of design parameters, such as length and vertical spacing of reinforcement, on the behaviour of the structure. In order to demonstrate, 11 models were tested, each one with different length of reinforcement or spacing. Each model was constructed and then placed in the centrifuge in order to artificially raise gravitational acceleration up to 35 g, reproducing the soil behaviour of a 5 metre high wall. Vertical and horizontal displacements were recorded by means of a special device which enabled tracking of deformations in the structure along its longitudinal cross section, essentially drawing its deformed shape. As expected, results confirmed reinforcement parameters to be the governing factor in the behaviour of earth reinforced structures since increase in length and spacing improved structural stability. However, the influence of the length was found out to be the leading parameter, reducing facial deformations up to five times, and the spacing playing an important role especially in unstable configurations. When failure occurred, failure surface was characterised by the same shape (circular) and depth, regardless of the reinforcement configuration. Furthermore, results confirmed the over-conservatism of codes, since models with reinforcement layers 0.4H long showed almost negligible deformations. Although the experiments performed were consistent and yielded replicable results, further numerical modelling may allow investigation on other issues, such as the influence of the reinforcement stiffness, facing stiffness and varying backfills.

Cosmological perturbations in generalized theories of gravity

The first part of the thesis concerns the study of inflation in the context of a theory of gravity called "Induced Gravity" in which the gravitational coupling varies in time according to the dynamics of the very same scalar field (the "inflaton") driving inflation, while taking on the value measured today since the end of inflation. Through the analytical and numerical analysis of scalar and tensor cosmological perturbations we show that the model leads to consistent predictions for a broad variety of symmetry-breaking inflaton's potentials, once that a dimensionless parameter entering into the action is properly constrained. We also discuss the average expansion of the Universe after inflation (when the inflaton undergoes coherent oscillations about the minimum of its potential) and determine the effective equation of state. Finally, we analyze the resonant and perturbative decay of the inflaton during (p)reheating. The second part is devoted to the study of a proposal for a quantum theory of gravity dubbed "Horava-Lifshitz (HL) Gravity" which relies on power-counting renormalizability while explicitly breaking Lorentz invariance. We test a pair of variants of the theory ("projectable" and "non-projectable") on a cosmological background and with the inclusion of scalar field matter. By inspecting the quadratic action for the linear scalar cosmological perturbations we determine the actual number of propagating degrees of freedom and realize that the theory, being endowed with less symmetries than General Relativity, does admit an extra gravitational degree of freedom which is potentially unstable. More specifically, we conclude that in the case of projectable HL Gravity the extra mode is either a ghost or a tachyon, whereas in the case of non-projectable HL Gravity the extra mode can be made well-behaved for suitable choices of a pair of free dimensionless parameters and, moreover, turns out to decouple from the low-energy Physics.

The relation between geometry and matter in classical and quantum gravity and cosmology

The present thesis is divided into two main research areas: Classical Cosmology and (Loop) Quantum Gravity. The first part concerns cosmological models with one phantom and one scalar field, that provide the `super-accelerated' scenario not excluded by observations, thus exploring alternatives to the standard LambdaCDM scenario. The second part concerns the spinfoam approach to (Loop) Quantum Gravity, which is an attempt to provide a `sum-over-histories' formulation of gravitational quantum transition amplitudes. The research here presented focuses on the face amplitude of a generic spinfoam model for Quantum Gravity.

Willem de Sitter in Leiden - ein Kapitel in der Rezeptionsgeschichte der Relativitätstheorien

Der niederländische Astronom Willem de Sitter ist bekannt für seine inzwischen berühmte Kontroverse mit Einstein von 1916 bis 1918, worin die relativistische Kosmologie begründet wurde. In diesem Kontext wird sein Name mit dem von ihm geschaffenen kosmologischen Modell verbunden, welches er als Gegenbeispiel zu Einsteins physikalischer Intuition schuf. Obwohl diese Debatte schon in wissenschaftshistorischen Arbeiten analysiert wurde, hat de Sitters Rolle in der Rezeption und dem Verbreiten der allgemeinen Relativitätstheorie bislang in der Hauptrichtung der Einstein-Studien noch nicht die ihr zustehende Aufmerksamkeit erhalten. Die vorliegende Untersuchung zielt darauf ab, seine zentrale Wichtigkeit für die Forschung zur ART innerhalb der Leidener Community aufzuzeigen. Wie Eddington war de Sitter einer der wenigen Astronomen, die sowohl hinreichende Ausbildung als auch nötige Interessen vereinten, um zum einen die spezielle und zum anderen die allgemeine Relativitätstheorie zu verfolgen. Er befasste sich zunächst 1911 mit dem Relativitätsprinzip (Einsteins erstes Postulat der SRT); zwei Jahre später fand er einen Nachweis für die Konstanz der Lichtgeschwindigkeit (Einsteins zweites Postulat). De Sitters Interesse an Gravitationstheorien reicht sogar noch weiter zurück und lässt sich bis 1908 zurückverfolgen. Überdies verfolgte er Einsteins Versuche, einen feldtheoretischen Ansatz für die Gravitation zu konstruieren, inklusive der kontroversen Einstein-Grossmann Theorie von 1913. Diese Umstände zeigen deutlich, dass de Sitters bekannteres Werk zur ART eine Konsequenz seiner vorausgegangenen Forschungen war und kein Resultat einer plötzlichen, erst 1916 einsetzenden Beschäftigung mit Einsteins Relativitätstheorie.

Quantum gravity effects in rotating black hole spacetimes

The aim of this work is to explore, within the framework of the presumably asymptotically safe Quantum Einstein Gravity, quantum corrections to black hole spacetimes, in particular in the case of rotating black holes. We have analysed this problem by exploiting the scale dependent Newton s constant implied by the renormalization group equation for the effective average action, and introducing an appropriate "cutoff identification" which relates the renormalization scale to the geometry of the spacetime manifold. We used these two ingredients in order to "renormalization group improve" the classical Kerr metric that describes the spacetime generated by a rotating black hole. We have focused our investigation on four basic subjects of black hole physics. The main results related to these topics can be summarized as follows. Concerning the critical surfaces, i.e. horizons and static limit surfaces, the improvement leads to a smooth deformation of the classical critical surfaces. Their number remains unchanged. In relation to the Penrose process for energy extraction from black holes, we have found that there exists a non-trivial correlation between regions of negative energy states in the phase space of rotating test particles and configurations of critical surfaces of the black hole. As for the vacuum energy-momentum tensor and the energy conditions we have shown that no model with "normal" matter, in the sense of matter fulfilling the usual energy conditions, can simulate the quantum fluctuations described by the improved Kerr spacetime that we have derived. Finally, in the context of black hole thermodynamics, we have performed calculations of the mass and angular momentum of the improved Kerr black hole, applying the standard Komar integrals. The results reflect the antiscreening character of the quantum fluctuations of the gravitational field. Furthermore we calculated approximations to the entropy and the temperature of the improved Kerr black hole to leading order in the angular momentum. More generally we have proven that the temperature can no longer be proportional to the surface gravity if an entropy-like state function is to exist.

Forecasts on the dark energy anisotropic stress for the esa euclid survey

The cosmological constant Λ seems to be a not satisfactory explanation of the late-time accelerated expansion of the Universe, for which a number of experimental evidences exist; therefore, it has become necessary in the last years to consider alternative models of dark energy, meant as cause of the accelerated expansion. In the study of dark energy models, it is important to understand which quantities can be determined starting from observational data, without assuming any hypothesis on the cosmological model; such quantities have been determined in Amendola, Kunz et al., 2012. In the same paper it has been further shown that it is possible to estabilish a relation between the model-independent parameters and the anisotropic stress η, which can be also expressed as a combination of the functions appearing in the most general Lagrangian for the scalar-tensor theories, the Horndeski Lagrangian. In the present thesis, the Fisher matrix formalism is used to perform a forecast on the constraints that will be possible to make on the anisotropic stress η in the future, starting from the estimated uncertainties for the galaxy clustering and weak lensing measurements which will be performed by the European Space Agency Euclid mission, to be launched in 2020. Further, constraints coming from supernovae-Ia observations are considered. The forecast is performed for two cases in which (a) η is considered as depending from redshift only and (b) η is constant and equal to one, as in the ΛCDM model.

Development and characterization of micromachined devices for separation techniques

Nowadays microfluidic is becoming an important technology in many chemical and biological processes and analysis applications. The potential to replace large-scale conventional laboratory instrumentation with miniaturized and self-contained systems, (called lab-on-a-chip (LOC) or point-of-care-testing (POCT)), offers a variety of advantages such as low reagent consumption, faster analysis speeds, and the capability of operating in a massively parallel scale in order to achieve high-throughput. Micro-electro-mechanical-systems (MEMS) technologies enable both the fabrication of miniaturized system and the possibility of developing compact and portable systems. The work described in this dissertation is towards the development of micromachined separation devices for both high-speed gas chromatography (HSGC) and gravitational field-flow fractionation (GrFFF) using MEMS technologies. Concerning the HSGC, a complete platform of three MEMS-based GC core components (injector, separation column and detector) is designed, fabricated and characterized. The microinjector consists of a set of pneumatically driven microvalves, based on a polymeric actuating membrane. Experimental results demonstrate that the microinjector is able to guarantee low dead volumes, fast actuation time, a wide operating temperature range and high chemical inertness. The microcolumn consists of an all-silicon microcolumn having a nearly circular cross-section channel. The extensive characterization has produced separation performances very close to the theoretical ideal expectations. A thermal conductivity detector (TCD) is chosen as most proper detector to be miniaturized since the volume reduction of the detector chamber results in increased mass and reduced dead volumes. The microTDC shows a good sensitivity and a very wide dynamic range. Finally a feasibility study for miniaturizing a channel suited for GrFFF is performed. The proposed GrFFF microchannel is at early stage of development, but represents a first step for the realization of a highly portable and potentially low-cost POCT device for biomedical applications.

I raggi di Einstein come strumento per la cosmologia

La Tesi presenta uno studio sulla distribuzione dei raggi di Einsten compiuta su campioni di ammassi simulati. Il codice utilizzato, MOKA, consente la costruzione di vasti campioni di ammassi in differenti cosmologie e con differenti parametri strutturali. I risultati ottenuti sono stati confrontati con quelli ottenuti dalla simulazione cosmologica N-body ad alta risoluzione MUSIC. Sono stati quindi prodotti campioni di ammassi per sette valori diversi della normalizzazione dello spettro di potenza e 7 valori diversi del parametro di densità della materia mantenendo la geometria piatta

Implications of regional fault distribution and kinematics for the uplift of rift flanks around the Rwenzori Mountains, Southwestern Uganda

Das Ziel dieser Arbeit bestand in der Untersuchung der Störungsverteilung und der Störungskinematik im Zusammenhang mit der Hebung der Riftschultern des Rwenzori Gebirges.rnDas Rwenzori Gebirge befindet sich im NNE-SSWbis N-S verlaufenden Albertine Rift, des nördlichsten Segments des westlichen Armes des Ostafrikanischen Grabensystems. Das Albertine Rift besteht aus Becken unterschiedlicher Höhe, die den Lake Albert, Lake Edward, Lake George und Lake Kivu enthalten. Der Rwenzori horst trennt die Becken des Lake Albert und des Lake Edward. Es erstreckt sich 120km in N-S Richtung, sowie 40-50km in E-W Richtung, der h¨ochste Punkt befindet sich 5111 ü. NN. Diese Studie untersucht einen Abschnitt des Rifts zwischen etwa 1°N und 0°30'S Breite sowie 29°30' und 30°30' östlicher Länge ersteckt. Auch die Feldarbeit konzentrierte sich auf dieses Gebiet.rnrnHauptzweck dieser Studie bestand darin, die folgende These auf ihre Richtigkeit zu überprüfen: ’Wenn es im Verlauf der Zeit tatsächlich zu wesentlichen Änderungen in der Störungskinematik kam, dann ist die starke Hebung der Riftflanken im Bereich der Rwenzoris nicht einfach durch Bewegung entlang der Graben-Hauptst¨orungen zu erklären. Vielmehr ist sie ein Resultat des Zusammenspiels mehrerer tektonische Prozesse, die das Spannungsfeld beeinflussen und dadurch Änderungen in der Kinematik hervorrufen.’ Dadurch konzentrierte sich die Studie in erster Linie auf die Störungsanalyse.rnrnDie Kenntnis regionaler Änderungen der Extensionsrichtung ist entscheidend für das Verständnis komplexer Riftsysteme wie dem Ostafrikanischen Graben. Daher bestand der Kern der Untersuchung in der Kartierung von Störungen und der Untersuchung der Störungskinematik. Die Aufnahme strukturgeologischer Daten konzentrierte sich auf die Ugandische Seite des Rifts, und Pal¨aospannungen wurden mit Hilfe von St¨orungsdaten durch Spannungsinversion rekonstruiert.rnDie unterschiedliche Orientierung spr¨oder Strukturen im Gelände, die geometrische Analyse der geologischen Strukturen sowie die Ergebnisse von Mikrostrukturen im Dünnschliff (Kapitel 4) weisen auf verschiedene Spannungsfelder hin, die auf mögliche Änderungen der Extensionsrichtung hinweisen. Die Resultate der Spannungsinversion sprechen für Ab-, Über- und Blattverschiebungen sowie für Schrägüberschiebungen (Kapitel 5). Aus der Orientierung der Abschiebungen gehen zwei verschiedene Extensionsrichtungen hervor: im Wesentlichen NW-SE Extension in fast allen Gebieten, sowie NNE-SSW Extension im östlichen Zentralbereich.rnAus der Analyse von Blattverschiebungen ergaben sich drei unterschiedliche Spannungszustände. Zum Einen NNW-SSE bis N-S Kompression in Verbindung mit ENE-WSW bzw E-W Extension wurde für die nördlichen und die zentralen Ruwenzoris ausgemacht. Ein zweiter Spannungszustand mit WNW-ESE Kompression/NNE-SSW Extension betraf die Zentralen Rwenzoris. Ein dritter Spannungszustand mit NNW-SSE Extension betraf den östlichen Zentralteil der Rwenzoris. Schrägüberschiebungen sind durch dazu schräge Achsen charakterisiert, die für N-S bis NNW-SSE Kompression sprechen und ausschließlich im östlichen Zentralabschnitt auftreten. Überschiebungen, die hauptsächlich in den zentralen und den östlichen Rwenzoris auftreten, sprechen für NE-SW orientierten σ2-Achsen und NW-SE Extension.rnrnEs konnten drei unterschiedliche Spannungseinflüsse identifiziert werden: auf die kollisionsbedingte Bildung eines Überschiebungssystem folgte intra-kratonische Kompression und schließlich extensionskontrollierte Riftbildung. Der Übergang zwischen den beiden letztgenannten Spannungszuständen erfolgte Schrittweise und erzeugte vermutlich lokal begrenzte Transpression und Transtension. Gegenw¨artig wird die Störungskinematik der Region durch ein tensiles Spannungsregime in NW-SE bis N-S Richtung bestimmt.rnrnLokale Spannungsvariationen werden dabei hauptsächlich durch die Interferenzrndes regionalen Spannungsfeldes mit lokalen Hauptst¨orungen verursacht. Weitere Faktoren die zu lokalen Veränderungen des Spannungsfeldes führen können sind unterschiedliche Hebungsgeschwindigkeiten, Blockrotation oder die Interaktion von Riftsegmenten. Um den Einfluß präexistenter Strukturen und anderer Bedingungen auf die Hebung der Rwenzoris zu ermitteln, wurde der Riftprozeß mit Hilfe eines analogen ’Sandbox’-Modells rekonstruiert (Kapitel 6). Da sich die Moho-Diskontinuität im Bereich des Arbeitsgebietes in einer Tiefe von 25 km befindet, aktive Störungen aber nur bis zu einer Tiefe von etwa 20 km beobachtet werden können (Koehn et al. 2008), wurden nur die oberen 25 km im Modell nachbebildet. Untersucht und mit Geländebeobachtungen verglichen wurden sowohl die Reihenfolge, in der Riftsegmente entstehen, als auch die Muster, die sich im Verlauf der Nukleierung und des Wachstums dieser Riftsegmente ausbilden. Das Hauptaugenmerk wurde auf die Entwicklung der beiden Subsegmente gelegt auf denen sich der Lake Albert bzw. der Lake Edward und der Lake George befinden, sowie auf das dazwischenliegende Rwenzori Gebirge. Das Ziel der Untersuchung bestand darin herauszufinden, in welcher Weise das südwärts propagierende Lake Albert-Subsegment mit dem sinistral versetzten nordwärts propagierenden Lake Edward/Lake George-Subsegment interagiert.rnrnVon besonderem Interesse war es, in welcherWeise die Strukturen innerhalb und außerhalb der Rwenzoris durch die Interaktion dieser Riftsegmente beeinflußt wurden. rnrnDrei verschiedene Versuchsreihen mit unterschiedlichen Randbedingungen wurden miteinander verglichen. Abhängig vom vorherrschenden Deformationstyp der Transferzone wurden die Reihen als ’Scherungs-dominiert’, ’Extensions-dominiert’ und als ’Rotations-dominiert’ charakterisiert. Die Beobachtung der 3-dimensionalen strukturellen Entwicklung der Riftsegmente wurde durch die Kombination von Modell-Aufsichten mit Profilschnitten ermöglicht. Von den drei genannten Versuchsreihen entwickelte die ’Rotationsdominierten’ Reihe einen rautenförmiger Block im Tranferbereich der beiden Riftsegmente, der sich um 5−20° im Uhrzeigersinn drehte. DieserWinkel liegt im Bereich des vermuteten Rotationswinkel des Rwenzori-Blocks (5°). Zusammengefasst untersuchen die Sandbox-Versuche den Einfluss präexistenter Strukturen und der Überlappung bzw. Überschneidung zweier interagierender Riftsegmente auf die Entwicklung des Riftsystems. Sie befassen sich darüber hinaus mit der Frage, welchen Einfluss Blockbildung und -rotation auf das lokale Stressfeld haben.

Black hole evaporation and stress tensor correlations

General Relativity is one of the greatest scientific achievementes of the 20th century along with quantum theory. These two theories are extremely beautiful and they are well verified by experiments, but they are apparently incompatible. Hints towards understanding these problems can be derived studying Black Holes, some the most puzzling solutions of General Relativity. The main topic of this Master Thesis is the study of Black Holes, in particular the Physics of Hawking Radiation. After a short review of General Relativity, I study in detail the Schwarzschild solution with particular emphasis on the coordinates systems used and the mathematical proof of the classical laws of Black Hole "Thermodynamics". Then I introduce the theory of Quantum Fields in Curved Spacetime, from Bogolubov transformations to the Schwinger-De Witt expansion, useful for the renormalization of the stress energy tensor. After that I introduce a 2D model of gravitational collapse to study the Hawking radiation phenomenon. Particular emphasis is given to the analysis of the quantum states, from correlations to the physical implication of this quantum effect (e.g. Information Paradox, Black Hole Thermodynamics). Then I introduce the renormalized stress energy tensor. Using the Schwinger-De Witt expansion I renormalize this object and I compute it analytically in the various quantum states of interest. Moreover, I study the correlations between these objects. They are interesting because they are linked to the Hawking radiation experimental search in acoustic Black Hole models. In particular I find that there is a characteristic peak in correlations between points inside and outside the Black Hole region, which correpsonds to entangled excitations inside and outside the Black Hole. These peaks hopefully will be measurable soon in supersonic BEC.

Observability of high density tracing molecular lines in lensed galaxies with the Atacama large millimeter array

Lo scopo di questo lavoro di tesi è indagare le capacità di ALMA di osservare il continuo e le righe molecolari di emissione di HCN, HCO+ e HNC, in galassie lensate ad alto z, nelle prime fasi della loro formazione. Per farlo vengono utilizzate osservazioni ALMA di righe di emissione molecolare, relative a dati pubblici di Ciclo 0. Queste osservazioni vengono utilizzate per simulare in modo realistico l’emissione da parte di galassie ad alto z e la risposta osservativa del telescopio, assumendo diverse possibili geometrie di lensing. Inoltre le recenti osservazioni ALMA sono state utilizzate per aggiornare le relazioni già esistenti tra la luminosità FIR e la luminosità delle righe molecolari. Queste recenti osservazioni con maggiore sensibilità e risoluzione angolare, sembrano essere in buon accordo con le precedenti osservazioni. Per realizzare questo progetto di tesi, sono stati scaricati dall’archivio ALMA i dati non calibrati relativi a due sorgenti ben studiate: NGC1614, rappresentativa delle galassie di tipo starburst ed IRAS 20551-4250, un AGN oscurato. Il processo di calibrazione è stato ripetuto per esaminare le proprietà dei cubi di dati utilizzando il pacchetto Common Astronomy Software Applications (CASA). Le righe spettrali osservate e l’emissione del continuo sono state successivamente estrapolate ad alto z riscalando adeguatamente le distanze, le dimensioni delle sorgenti e le frequenze di emissione. In seguito è stato applicato un modello di lensing gravitazionale basato su quello di Lapi et al. (2012). Sono state considerate diverse configurazioni tra lente e sorgente per ottenere diverse geometrie delle immagini e diversi fattori di amplificazione. Infine stato utilizzato il software CASA per simulare le osservazioni ALMA in modo da verificare le capacità osservative del telescopio al variare della geometria del sistema. Per ogni riga molecolare e per l’emissione del continuo sono state determinate la sensibilit e la risoluzione che possono essere raggiunte con le osservazioni ALMA e sono state analizzate alcune strategie osservative per effettuare survey di righe spettrali in oggetti lensati. Inoltre stata analizzata la possibilit di caratterizzare oggetti starburst ed AGN dai rapporti tra le righe di emissione delle molecole traccianti di alta densit. Le prestazioni di ALMA consentiranno di distinguere e stimare i contributi relativi di SB ed AGN in galassie lensate a z > 2.5, quindi vicine alla loro presunta epoca di formazione (Lapi et al. 2010), in meno di 5 minuti di osservazione per qualsiasi fattore di magnificazione. Nel presente lavoro sono state inoltre discusse alcune strategie osservative per condurre survey o followup per osservare le righe di HCN(4-3), HCO+(4-3) e HNC(4-3) in galassie lensate a redshift 2.5 < z < 3, dimostrando che sono possibili per campioni statisticamente significativi in tempi relativamente brevi.

Quantum Einstein gravity - advancements of heat kernel-based renormalization group studies

The asymptotic safety scenario allows to define a consistent theory of quantized gravity within the framework of quantum field theory. The central conjecture of this scenario is the existence of a non-Gaussian fixed point of the theory's renormalization group flow, that allows to formulate renormalization conditions that render the theory fully predictive. Investigations of this possibility use an exact functional renormalization group equation as a primary non-perturbative tool. This equation implements Wilsonian renormalization group transformations, and is demonstrated to represent a reformulation of the functional integral approach to quantum field theory.rnAs its main result, this thesis develops an algebraic algorithm which allows to systematically construct the renormalization group flow of gauge theories as well as gravity in arbitrary expansion schemes. In particular, it uses off-diagonal heat kernel techniques to efficiently handle the non-minimal differential operators which appear due to gauge symmetries. The central virtue of the algorithm is that no additional simplifications need to be employed, opening the possibility for more systematic investigations of the emergence of non-perturbative phenomena. As a by-product several novel results on the heat kernel expansion of the Laplace operator acting on general gauge bundles are obtained.rnThe constructed algorithm is used to re-derive the renormalization group flow of gravity in the Einstein-Hilbert truncation, showing the manifest background independence of the results. The well-studied Einstein-Hilbert case is further advanced by taking the effect of a running ghost field renormalization on the gravitational coupling constants into account. A detailed numerical analysis reveals a further stabilization of the found non-Gaussian fixed point.rnFinally, the proposed algorithm is applied to the case of higher derivative gravity including all curvature squared interactions. This establishes an improvement of existing computations, taking the independent running of the Euler topological term into account. Known perturbative results are reproduced in this case from the renormalization group equation, identifying however a unique non-Gaussian fixed point.rn