Semi-classical aspects of black hole physics are studied with particular emphasis on Hawking radiation and its derivation from tunnelling method techniques.

In this work we discuss some specific features related to the concept of singularity in the gravitational theory. We give a brief review of some various definitions for singularity, then we explore some "negative" results, in the sense they are not able to reproduce, in general, a regular solution. We present some of these approaches, namely the non-commutative geometry; the Non-Linear Electrodynamics; and the conformal approach. We later generalize these results into a no-go theorem, which is actually a fully original result. In the second part of this work, we discuss some working examples of regular solutions: we present three of them already present in literature (non-minimal Yang-Mills coupling, mimetic field approach and non-polynomial gravity), then we use such results to build up a model of a regular cosmological solution. Its generating mechanism and its main features are described, replacing the Big Bang with a bounce; the inflationary behavior at large time is also recovered. In the following two chapters, we present some different schemes to build regular solutions from the coupling between gravity and a scalar field. In particular, in chapter 7, we use a minimal coupling, while in chapter 8 we find some sufficient (though not necessary) conditions to build a regular solution, within the framework of the Horndeski theory. In both cases we are not able to find explicit results. In the ninth chapter we discuss a model of a regular black hole, coupling gravity with some fluid: in this case, an exact solution is found. We prove it is regular and we show some of its general features; we also discuss the time-dependent case, although we are only able to discuss its asymptotic behavior. We also discuss some of its problems, mainly due to instability. In the appendices we try to extend the no-go theorem to $F(R)$ theories and try to solve the instabilities of the fluid approach respectively.

Already in ancient Greece, the pre-Socratic philosophers thought that natural phenomena, although different, were homogeneous, of the same fundamental nature. In their theories can be found the search for a common reference point (arché) that puts order in the chaotic multiplicity of phenomena. After Albert Einstein’s theory of gravitation (General Relativity -GR-) was published in 1915, the search for a unified field theory that combines gravity with electromagnetism began to become serious. It seemed plausible that there were no other fundamental forces. The main contributors were Gunnar Nordstrom, Hermann Weyl, Arthur Eddington, Theodor Kaluza, Oskar Klein (See Theory of Kaluza-Klein, 1921) and most notably the many attempts by Einstein and his collaborators. No attempt went through. In the first half of the twentieth century quantum mechanics was consolidated, an instrument capable of overcoming the inadequacy of classical mechanics to explain phenomena and properties such as blackbody radiation, the photoelectric effect, the specific heat of solids, the atomic spectra, the stability of atoms, the Compton effect, .... When in the thirties Fermi and Yukawa ’s studies led to the discovery of nuclear forces, the quantum formalism proved to be appropriate for the description of the new phenomena and, in 1967-68, Sheldon Glashow, Steven Weinberg and Abdus Salam showed how the weak nuclear force and the electromagnetism were simply different manifestations of the same force (electroweak). Since then, proposals have been done to include in a single grand unification theory also the strong nuclear force, and some of them (GTU SU(5) and SO(10)) have provided testable predictions as the quantization of electric charge. At classical level there is an extension of the Kaluza-Klein theory on a 11-dimensional space M4 × S1 × S2 × CP2. It corresponds to Einstein’s General Relativity with 7 extra dimensions, and considers all four forces as different expressions of a “mega†gravitational field. The forces are unified at the classical level but, once quantized, the theory turns out to be inconsistent and therefore unusable. This is because the nuclear forces have range of 10−15 m for strong force and of 10−18 m for weak force, distances at which classical physics loses its meaning. Ultimately, it seems that quantum mechanics is compatible with electroweak and strong interactions only if we limit ourselves to spaces of dimensionality less than or equal to 4. In addition, it is inconsistent with General Relativity for spaces with more of 3 dimensions. For these reasons, the theory of Kaluza-Klein fails doubly. Really, the incompatibility is not between general relativity and quantum mechanics in its entirety, but rather between General Relativity and the method of calculation used in quantum mechanics: perturbative expansion whose terms, in the cases indicted above, become . To get around this problem two different approaches have been taken: String Theory and Loop Quantum Gravity. The first has completely changed the wording of quantum theory, from considering local interactions, where the phenomena occur at specific points (of Feynman graphs), to interactions “extended†, where the phenomena are distributed along one limited dimension (string), open or closed. This system has eliminated the divergences in the terms of perturbative expansion, but has developed other anomalies, eliminated only by building up the theory on a space of 11 dimensions. Unfortunately, the extra dimensions introduce a huge number of arbitrariness, such as the theory can predict everything and nothing. The scientific community hopes to identify some potential whose minimum make a selection between these arbitrariness, but we are still far from such a result. The alternative discussed in this thesis is the Loop Quantum Gravity. This is simply the union of GR and quantum mechanics, without modifying the basic axioms of both. It can be made only in spaces of dimensionality equal to 4 and it surrenders completely the perturbative expansion. This produces fascinating predictions, such as the inflation of early universe, and the lack of singularities in the black holes and in the big bang. It also provides the picture of a “combinatorial†universe, described by nodes connected by paths, whose only necessary variables are integer numbers associated with nodes and paths. This last point in particular escapes the string theory which, whilst losing the locality, is however concentrated within the “very small†. The Loop Quantum Gravity, by contrast, is able to describe the universe as a whole, and to deal with transitions between universes of different topology. The downside is that the calculations are so complex that they are impracticable. Strategies have been developed to introduce a different perturbative expansion that makes the calculations feasible, but this introduces important changes to the initial structure of the theory, in a way that eliminate the beautiful cosmological predictions. Nevertheless, we tried to calculate the graviton propagator in this new “modified framework†, and the result is compatible with linearized quantum GR . For this reason, this framework has not been abandoned. It also seems that this formalism can easily be extended to include extra-dimensions and adapted to the unified theory of Kaluza Klein. This thesis has been developed in an attempt to contribute to the desire for simplification and connection to the essence that has always been in the natural sciences. In particular, it was given a demonstration of how the †modified framework†of Loop Quantum Gravity is derivable from a classical formulation of the GR of Palatini type. Finally, we give suggestions for extending the model to 11 dimensions, because 11 is the number suggested by String theory, by the classical theory of Kaluza Klein, and by the GTU SO(10). Probably the truth lies somewhere in between, maybe an action of a 4-dimensional brane immersed in a 11-dimensional universe would be the right compromise between String Theory and Loop Quantum Gravity. A 4-dimensional brane represents our universe, and any contact with other branes of a much smaller scale put small pieces of it in vibration. Depending on the number of dimensions in which contact is, the part could be a vibrating string or a two- or three-brane (with probability decreasing rapidly moving from string to the three-brane). So, we even lose the distinction between the notions of particles and universes, making the first totally unnecessary. The action of a 4-brane is equivalent to the action of Loop Quantum Gravity, with the coordinate-fields which assume the role of gauge fields, and the indexes in the 11-dimensional space that would become similar to the indexes of internal gauge. This thesis focuses on two specific problems: the calculation of the graviton propagator in Loop Quantum Gravity and the derivation of the “modified framework†from the Palatini formulation of GR (Chapter 8). While the first it was simply supported with a minimum contribution, the second is a problem undertaken by the student in a completely independent way that, while waiting for more in-depth audits, has not yet shown any inconsistency and for now can be hailed a success. A small space is reserved for some inedited consideration undertaken by the student on the “physical†projector. This operator is intended to project the Hilbert space of kinematic states in the subspace of physical states. The conclusion of the argument is simple and somewhat disturbing: the Loop Quantum Gravity is not an unitary theory!

The aim of this work is to investigate the both, some mathematical and physical general aspect of modified gravity, and, more specifically, the proprieties of viable, realistic models of modified gravity which can be used to reproduce the inflation and the dark energy epoch of universe today.

One of the most interesting problems in string theory is to understand how the background space-time on which the string propagates arises in a self-consistent way. For open strings, there are two main approaches to this problem, boundary string field theory (BSFT) and cubic string field theory (CSFT). In the first part of this Thesis we deal with the construction of the spacetime tachyon effective action in BSFT. Renormalization fixed points are solutions of classical equations of motion and should be viewed as solutions of classical string field theory. We have constructed the Witten-Shatashvili (WS) space-time action S and shown that some solitonic solutions are lower dimensional D-branes for which the finite value of S provides a quite accurate prediction of the D-brane tension. We have derived the explicit relation between the CSFT and WS action as a field redefinition which is nonsingular on-shell only when the normalization factor in the WS action coincides with the tension of the D25-brane, in agreement with the conjectures involving tachyon condensation. We have also found a time-dependent solution of CSFT whose evolution is driven by a diffusion equation that makes the equations of motion local with respect to the time variable. The analysis here proposed has attracted a good deal of attention for its potential cosmological applications. The profile can be expressed in terms of a series in powers of exponentials of the time coordinate, and gives evidence of a well-defined but wildly oscillatory behavior. The tachyon rolls well past the minimum of the potential, then turns around and begins to oscillate with ever increasing amplitude. Furthermore, we have derived an analytic series solution of the elliptic equations providing the 4-tachyon off-shell amplitude. From such a solution we computed the exact coefficient of the quartic effective action relevant for time-dependent solutions and we derived the exact coefficient of the quartic tachyon coupling. We studied the rolling tachyon solution expressed as a series of exponentials of the time coordinate both using level-truncation computations and the exact 4-tachyon amplitude. The results for the level-truncated coefficients converge to those derived using the exact string amplitude and confirm the wild oscillatory behavior. In the second part of the Thesis we consider the extension of the gauge/gravity correspondence to systems with reduced and hence more realistic supersymmetry, which is one of the main steps towards a non-perturbative description of confining, QCD-like, gauge theories in terms of gravitational backgrounds. If string theory on AdS5xS5 is integrable, the theory on simple orbifolds of that space would also be expected to be integrable. We have computed the planar finite size corrections to the spectrum of the dilatation operator acting on states of a certain limit of conformal N = 2 quiver gauge field theory which is a ZM-orbifold of N = 4 SYM theory. We matched the result to the string dual, IIB superstrings on a pp-wave background with a periodically identified null coordinate. Up to two loops, we have shown that the computations done by using an effective Hamiltonian technique and a twisted Bethe Ansatz agree with each other and also agree with a computation of the analogous quantity in string theory. Our results are consistent with integrability of the N = 2 theory.

This thesis is devoted to the study of the hydrodynamic behavior of the unitary Fermi gas trapped by a highly elongated harmonic potential. Propagation of sound is one of the most exciting features exhibited by interacting many-body systems. It provides crucial information on the dynamic behavior of the system as well as on key thermodynamic quantities. The propagation of sound is particularly interesting in superfluids where two-fluid hydrodynamic theory predicts the occurrence of two different sounds: first sound, where the normal and superfluid component oscillate in phase, and second sound, where the two components oscillate with opposite phase. In the thesis, we investigate the propagation of sound waves of the unitary Fermi gas in a cylindrical geometry by solving the equations of two-fluid hydrodynamics in the `1D' scenario at finite temperature. The relevant thermodynamic functions entering the hydrodynamic equations are discussed in the superfluid and normal regimes in terms of universal scaling functions. Both the first sound and second sound solutions are calculated as a function of temperature and the role of the superfluid density is explicitly pointed out. The density fluctuations in the second sound wave are found to be large enough to be measured as a consequence of the finite thermal expansion coefficient of the gas, which is the strategy used in a recent experiment carried out at Innsbruck where second sound was detected in the unitary Fermi gas. We also provide an investigation of the temperature dependence of the collective oscillations of first sound nature exhibited by a highly elongated harmonically trapped Fermi gas at unitarity, including the region below the critical temperature for superfluidity. Differently from the lowest axial breathing mode, the hydrodynamic frequencies of the higher-nodal excitations show a temperature dependence, which is calculated starting from Landau two-fluid theory and using the available experimental knowledge of the equation of state.

L'obbiettivo di questa tesi è di investigare il ruolo della formazione delle aspettative nei modelli macroeconomici basati su agenti e stock-flussi coerenti. Mentre ci sono stati notevoli passi avanti nello sviluppo di tali modelli, la ricerca sulla formazione e sul ruolo delle aspettative in essi rimane ancora poco sviluppato. La tesi è composta da tre articoli, ognuno dei quali si focalizza sulla formazione delle aspettative in un settore economico speci co e presenta una serie di esperimenti riguardanti la variazione dei meccanismi di formazione delle aspetta- tive, dinamiche di opinioni e sentimenti, così come le applicazioni delle politiche economiche. La tesi dimostra l'influenza potenzialmente forte delle aspettative dei agenti sulla volatilità macroeconomica e mostra che, dipendendo dalla loro speci cazione e l'ambiente economico, le aspettative possono essere sia un elemento stabilizzante che un elemento destabilizzante. Inoltre, attraverso l'ampia gamma di esperimenti politici condotti, serve a sottolineare il ruolo importante delle politiche stabilizzanti nei sistemi che esibiscono fluttuazioni endogene, e il capitolo 4 in particolare mette in evidenza la potenziale dipendenza dell'efficacia delle politiche economiche dalle aspettative. Allo stesso tempo, alcuni dei risultati ottenuti avvertono che nei sistemi complessi, gli interventi politici devono essere calibrati attentamente affinché non diventino essi stessi fonte di instabilità. / The purpose of this thesis is to investigate the role of expectations formation in agent-based and stock-flow consistent macroeconomic models. While there have been considerable advances in the development of such models, research on the formation and role of beliefs and expectations within them remains underdeveloped. The thesis consists of three papers, each of which focuses on expectations formation in one particular economic sector and presents a range of experiments concerning the variation of expectations formation mechanisms, belief and sentiment dynamics, as well as policy applications. The thesis demonstrates the potentially strong influence of agents' expectations on macroeconomic volatility and shows that depending on their specification as well as the economic environment, expectations can be both a stabilising and destabilising factor. Moreover, through the wide range of policy experiments conducted, it serves to emphasise the important role of stabilisation policies in systems exhibiting endogenous fluctuations and chapter 4 in particular highlights the potential dependence of policy effectiveness on expectations. At the same time, some of the obtained results caution that in complex systems, policy interventions must be carefully calibrated lest they themselves become a source of instability.

Fusarium graminearum causa la fusariosi della spiga nei cereali a paglia. Il fungo produce sia conidi che ascospore sui residui della coltura precedente, le ascospore sono prodotte in periteci. La produzione e maturazione di periteci e ascospore in risposta a diverse condizioni di temperatura e umidità relativa sono state studiate. Dato che le condizioni atmosferiche influenzano anche l’umidità del substrato su cui l’inoculo è prodotto, la relazione tra i fattori atmosferici e l’umidità dei residui colturali di mais è stata esaminata. I fattori atmosferici influenzano anche il rilascio delle ascospore. L’effetto della temperatura è stato studiato in vitro. Mediante esperimenti in condizioni naturali, sono state definite regole per l’individuazione di condizioni favorevoli al rilascio di ascospore sulla base di pioggia e deficit di pressione di vapore. La distribuzione delle ascospore e dei conidi all’interno della vegetazione del frumento è quindi stata studiata mediante l’uso di captaspore passivi. Le ascospore possono essere rilasciate e depositarsi sulle spighe in condizioni non favorevoli per la germinazione. La germinazione di ascospore sottoposte a periodi asciutti di diversa durata, e a diverse condizioni di temperatura e umidità relativa durante il periodo asciutto, è stata studiata sia in vitro che in planta. / Fusarium graminearum causes Fusarium head blight of small-grain cereals. The fungus produces conidia and ascospores on the previous crop residues, ascospores are formed in perithecia. Production and maturation of perithecia and ascospores at several temperature and relative humidity conditions were studied. As environmental conditions also influence the moisture content of the substrate on which inoculum is produced, the relationship between environmental factors and moisture of maize residues was assessed. Environmental factors also influence ascospore discharge. The effect of temperature was studied in vitro. Experiments in natural condition allowed to define rules for conditions leading to ascospore discharge, based on rain and vapor pressure deficit. Once discharged, the distribution of ascospores and conidia in the wheat canopy was studied using passive spore traps. Ascospores can be discharged and deposit on wheat spikes also in conditions that are unfavorable for germination. Germination of ascospores incubated in dryness for periods of several length, in several condition of temperature and relative humidity during dryness, was studied both in vitro and in planta.

No description available.

E’ stato affrontato in modo approfondito lo studio dei campi gravitazionali della relatività generale (RG) che producono un’accelerazione uniforme, e si è confrontato tale studio con i sistemi si riferimento (SR) accelerati della relatività ristretta (RR). Nel corso di quest’analisi sono stati trovati alcuni aspetti non evidenziati in precedenza nella letteratura scientifica, di cui il più rilevante è il fatto che la metrica di Rindler produce un campo che, osservato con misure di tipo radar, appare uniforme a un osservatore solidale con il campo stesso. Si è inoltre trovata più di una metrica cui corrisponde un’accelerazione che non dipende dalla coordinata di partenza. Per il campo di Rindler è stata eseguita anche un’analisi approfondita, tramite un’applicazione diretta del principio di equivalenza (PE). La metodologia utilizzata e i risultati sono un contributo originale di questa tesi e sono di interesse da un punto di vista didattico. Nel corso dell’analisi delle proprietà del campo di Rindler sono stati analizzati in modo operativo: il confronto del ritmo di marcia di due orologi che si trovano a una quota differente, la deflessione dei raggi luminosi e la traiettoria di un corpo in caduta libera. Infine si è indagato sulla forma della metrica di una distribuzione di massa a simmetrica planare.