Σχεδόν τέσσερις δεκαετίες πριν, η μαθηματική αναλογία μεταξύ των νόμων της μηχανικής των μελανών οπών και των νόμων της θερμοδυναμικής έδωσε ισχυρά επιχειρήματα στους Bekenstein και Hawking να υποθέσουν ότι, αν τα κβαντικά φαινόμενα λαμβάνονται υπόψη, οι μελανές οπές θα πρέπει να θεωρηθούν ως θερμοδυναμικά συστήματα, που χαρακτηρίζονται από θερμοκρασία και την εντροπία τους. Πιο συγκεκριμένα, ότι η εντροπία των μελανών οπών είναι S = A / 4, όπου Α είναι η περιοχή του ορίζοντα γεγονότων. Ακόμη και σήμερα, υπάρχουν δύο σημαντικά ερωτήματα σχετικά με τους βαθμούς ελευθερίας: α) ποιοι είναι οι βαθμοί ελευθερίας υπεύθυνοι για την εντροπία των μελανών οπών; β) που βρίσκονται αυτοί οι βαθμοί ελευθερίας; Πριν από τριάντα χρόνια, η απάντηση και στα δύο παραπάνω ερωτήματα ήταν: "Δεν γνωρίζουμε" Σήμερα, αντίθετα, το πρόβλημα είναι ότι, υπάρχουν πάρα πολλές απαντήσεις για τα παραπάνω ερωτήματα. Σε εργασία αυτή, μελετώ την παραγωγή των Bekenstein-Hawking φόρμουλα για την εντροπίας των μελανών οπών στην κβαντική θεωρία της βαρύτητας. Ειδικότερα, επικεντρώνομαι στις υποθέσεις, τη μεθοδολογία και τα αποτελέσματα κάθε προσέγγισης. Πρώτα, μελετώ την παραγωγή της Bekenstein-Hawking φόρμουλα σε μεθόδους που δεν βασίζονται σε μια θεμελιώδη θεωρία της κβαντικής βαρύτητας, όπως η στατιστική μηχανική προέλευση της εντροπίας μιας περιστρεφόμενης, φορτισμένη μελανής οπής, η μέθοδος του ολοκληρώματος διαδρομών στο πλαίσιο της Ευκλείδεια κβαντική βαρύτητα και τη μέθοδος του κανονικού συνόλου για τις μελανές οπές σε μια σφαιρική κοιλότητα στο πλαίσιο της Ευκλείδεια κβαντικής βαρύτητας. Τα τελευταία είκοσι χρόνια περίπου, oι αποδείξεις γίνονται στα πλαίσια θεμελιωδών θεωριών της κβαντικής βαρύτητας. Εδώ, θα δούμε την απόδειξη στα πλαίσια της σύμμορφης θεωρίας πεδίου του ορίζοντα, της επαγόμενης βαρύτητας, της κβαντικής βαρύτητας των βρόγχων και της θεωρίας των χορδών. / Almost four decades ago, the mathematical analogy between the laws of black hole mechanics and the laws of thermodynamics gave strong arguments to Bekenstein and Hawking to assume that, if quantum effects are taken into account, black holes should be viewed as thermodynamic systems, characterized by temperature and entropy. In particular, that the black hole entropy is S=A/4, where A is the area of the event horizon. Even today, there are two important questions about the degrees of freedom: a) which are the degrees of freedom responsible for the black hole entropy? b) Where are the degrees of freedom localized? Thirty years ago, the answer to both questions above was: "we do not know". Today, by contrast, the problem is that, there are too many answers for the questions above. In this thesis, I study the derivation of the Bekenstein-Hawking formula for the black hole entropy in quantum gravity theories. In particular, I focus on the hypotheses, the methodology and the results of each approach. First, I consider the derivation of the Bekenstein-Hawking formula in methods which are not based on a fundamental theory of quantum gravity such as, the statistical mechanical origin of the entropy of a rotating, charged black hole, the path integral method in the Euclidean quantum gravity framework and the canonical ensemble method for black holes in a spherical cavity in the Euclidean quantum gravity framework. Then, I consider the derivations of the black hole entropy which are made in the framework of candidate quantum gravity theories such as, the horizon conformal field theory, the induced gravity theory, loop quantum gravity and string theory.

General relativity describes gravity in terms of an interacting massless spin-2 field - the graviton. This 100-year-old theory has been spectacularly successful in explaining observations. However, theoretical exploration and the cosmological constant problem motivate the study of alternative theories of gravity. Recently, there has been great progress in understanding theories that give the graviton a mass. This thesis considers several aspects of these massive spin-2 effective field theories and related theories. These theories are first studied from the perspective of scattering amplitudes. The most general 2 → 2 scattering amplitude is constructed for theories containing a single massive graviton or vector. These amplitudes are then used to find the highest strong coupling scales in such theories, assuming a particular scaling of fields and momenta. Generalisations to include additional fields and self-interactions for massive higher-spin fields are also discussed. Constraints that arise from the existence of an ultraviolet completion are then studied. It is shown using dispersion relation arguments that the pseudo-linear massive spin-2 theory cannot admit an analytic, Lorentz-invariant, and unitary ultraviolet completion, but that such completions are not ruled out for massive vector theories. The behaviour of massive spin-2 theories under dimensional reduction is also explored. Stability conditions and the lower-dimensional spectrum are derived for the Kaluza-Klein dimensional reduction of a partially massless graviton and a massive graviton on an Einstein product manifold. Additionally, the nonlinear dimensional reduction of the zero modes in dRGT massive gravity is shown to produce a mass-varying massive gravity theory. Lastly, attempts to construct a version of unimodular gravity containing a massive graviton are discussed. A candidate theory is proposed and is shown to have pathologies. Dimensional reduction is then used to generate massive spin-2 theories with noncanonical kinetic terms and auxiliary fields. These theories are shown to be equivalent to the Fierz-Pauli theory, which provides further evidence for the uniqueness of the kinetic term used in dRGT massive gravity.

This thesis attempts to test several frameworks of non-Newtonian gravity in the context of galaxies and galaxy clusters. The theory most extensively discussed was that of Modified Newtonian Dynamics (MOND) with Galileon gravity, Emergent Gravity (EG) and Modified Gravity (MOG) mentioned to a lesser extent. Specifically, the main focus of this thesis was to determine whether MOND and MOND-like theories were compatible with galaxy cluster data, without the need to include cold dark matter. To do this, the paradigms of Extended MOND (EMOND), Generalised MOND (GMOND) and superfluid dark matter were investigated. The theories were outlined and applied to galaxy cluster data. The main findings of this were that EMOND and GMOND had some success with explaining galaxy cluster mass profiles, without requiring an additional dark matter component. The superfluid paradigm also enjoyed some success in galaxy clusters, which was expected as it behaves in a similar manner to the standard cold dark matter paradigm in cluster environments. However, the superfluid paradigm may have issues in the very centre of galaxy clusters due to the theory predicting constant density cores, whereas the cold dark matter paradigm predicts density cores which are cuspier. The EMOND paradigm was also tested against ultra-diffuse galaxy (UDGs) data as they appear in cluster environments, where EMOND becomes important. It was found that EMOND can reproduce the inferred mass of the UDGs, assuming they lie on the fundamental manifold (FM). The validity of the assumptions used to model the UDGs are discussed in the text. A two-body problem was also conducted in the Galileon gravity framework. The amount of additional gravitational force, compared to Newtonian was determined for a small galaxy at the edge of a galaxy cluster.

No description available.

Today, regional and foreign trade is inevitable for a geographically small country like Georgia where resources and markets for sustainable and economic growth are limited. The role of agricultural exports in the economic performance of Georgia was clearly demonstrated by the experience of the collapse of the national economy after independence from the Soviet Union, when Georgian farmers lost the export potential to former Soviet Union countries. As one of the tools, which struggles to re-start agricultural production and trade, in recent years, Georgian countryside experiences abrupt increase in number of agricultural cooperatives that are being established as a result of joint endeavor of international programs and Georgian government. For local farmers, who typically hold small plots of fragmented land, cooperatives are promoted as a tool for better market access and consequently increase of income and poverty reduction. The crucial product, with traditionally highest potential for exports is wine. Georgia, a country located between Caspian Sea and Black sea is also known as cradle of wine. Country's wine industry wants to diversify the markets and expand the export potential. The proposed dissertation thesis will evaluate the Constraints and opportunities of small farmers' market access in Georgia. The whole research is based on econometric time series techniques Granger causality, Co-integration test, Gravity Model, Probit Model, and first-hand experience through personal interviews of authors with members of cooperatives. The results from the research will have important implications for policy-makers in order to implement appropriate growth and development strategies of agriculture and to agricultural trade.

In Nepal, the harsh mountainous topography hinders a viable transport infrastructure, including roads, making trails and mule tracks the only available option for a majority of the population. This isolates communities and compels them to face an exhausting, time consuming and often dangerous journey to get their agricultural products to the nearest markets. This study investigates the potential of gravity goods ropeway as a viable means of transportation to serve these isolated communities. This research looks at Hiklung village to explore the significance of gravity good ropeways in linking farmers to markets, its socio-economic impact, and its effectiveness in improving food security and livelihoods of project beneficiaries. The findings of this study, based on participant observation and interactions with project beneficiaries, suggest that an alternative means of transportation like gravity goods ropeway can be a sustainable transport solution to these isolated communities and increase their participation in the local economy.

In this research the Bring-Jerrard quintic polynomial equation is investigated for a formula. Firstly, an explanation given as to why finding a formula and the equation being unsolvable by radicals may appear contradictory when read out of context. Secondly, the reason why some mathematical software programs may fail to render a conclusive test of the formula, and how that can be corrected is explained. As an application, this formula is used to determine another formula that expresses the gravitational constant in terms of other known physical constants. It is also explained why up to now it has been impossible to determine this expression using the current underlying theoretical basis. / M. Sc. (Applied Mathematics)

This thesis investigates the effect of US development aid on US exports to 134 recipient countries over the time period 1993 to 2015 with an application of the gravity model of international trade. Estimates of one-way panel dataset, specified by a dummy approach and estimated with OLS and PPML, suggest that for every aid dollar spent by the United States, US exports significantly increase by 1.59 US dollar. By lagging the aid variable for several years after disbursement, we find a declining effect of US aid on US exports, which indicates that tied aid is an important channel of the effect's magnitude. The effect does not vary systematically across income groups. Yet for geographical regions with a higher US export share, the impact of US aid on US exports is significantly larger suggesting that existing trading relations contribute to a larger effect of aid on donor's exports. The evidence shows that US aid increases US exports and reinforces economic relations with recipient countries and, thus, can be regarded as an important motive for the donor to provide development aid.

Orientador: Antonio Accioly / Banca: José Geraldo Pereira / Banca: José Wadih Maluf / Banca: Ilya Lvovich Shapiro / Banca: João Barcelos Neto / Resumo: A gravitação quadrática em (2 + 1)D, ao contrário da gravitação tridimensional de Einstein, é localmente não trivial e possui um potencial extremamente bem comportado. Analisa-se esta teoria neste trabalho. Obtém-se a solução geral das equações de campo linearizadas numa versão tridimensional do gauge de Teyssandier, e a partir desta encontra-se a solução geral no caso de uma fonte pontual estática. Esta métrica se assemelha à métrica quadridimensional relativa a uma corda cósmica reta com simetria de gauge do tipo U(1). Existe uma força gravitacional atuando sobre uma partícula teste movendo-se em baixa velocidade, o que não acontece no contexto da relatividade geral em (2 + 1)D, e raios luminosos sofrem deflexão gravitacional. Considera-se também as mudanças que ocorrem quando um termo topológico de Chern-Simons é adicionado à gravitação quadrática em (2 + 1)D. Acha-se que o inofensivo modo escalar massivo da última, dá origem a um problemático ghost massivo de spin O, enquanto que o ghost massivo de spin 2 é substituído por duas partículas físicas massivas, ambas de spin 2 / Abstract: Quadratic gravity in (2 +1)D, unlike three-dimensional Einstein's gravity, is locally nontrivial and has an extremely well-behaved potential. Here we consider this theory. The general solution of the linearized field equations in a three-dimensional version of the Teyssandier gauge is obtained, and from that the solution for a static pointlike source is found. This metric greatly resembles the four-dimensional metric of a straight U(1)-gauge cosmic string in the framework of linearized quadratic gravity. It is found that a gravitational force is exerted on a slowly moving test particle, a feature not present in general relativity in (2 + 1)D. The deflection of light rays is analyzed as well. We also consider the changes that occur when a topological Chern-Simons term is added to quadratic gravity in (2 + 1)D. It is found that the harmless massive scalar mode of the latter gives rise to a troublesome massive spin-0 ghost, while the massive apin-2 ghost is replaced by two massive particles both of spin-2 / Doutor

Neste trabalho, analisamos o modelo de gravitação dilatônica proposto por Callan, Giddings, Harvey e Strominger (modelo de CGHS). Aplicamos a teoria de vínculos ao modelo e mostramos que só existem vínculos de primeira classe. Em seguida ap0licamos a técnica de BRST-BFV para quantizar a teoria. Mostramos que os fantasmas na função de partição estão desacoplados dos campos e podem ser integrados. Utilizamos uma transformação canônica para escrever os vínculos na forma quadrática, que facilita a quantização da teoria. Para completar a quantização usamos o procedimento de Dirac para obter a álgebra dos vínculos expressa na forma do tensor momento-energia. Existe uma anomalia na álgebra que é apropriadamente eliminada quando adicionamos um termo de improvement à ação. Finalmente usamos o procedimento de Dirac para obter soluções para a função de onda. Isto prova que a teoria de CGHS em duas dimensões é perfeitamente quantizável. / We analyse a theory of gravitation in two dimensions using the hamiltonian formalism. For this purpose we use the CGHS model in the conformal gauge. The theory of constraints shows that we have only first-class constraints. After that, we apply the BRST-BFV technique to quantize the theory. We show that the ghosts in the partition function are decoupled from the fields. Then we integrate the ghosts in the partition function. By a suitable canonical transformation we write the constraints in a quadratic form which facilitates the quantization of the theory. To complete the quantization we use the Dirac procedure to obtain the constraints algebra expressed in the energy-momentum tensor form. There is an anomaly in the algebra which can be suitably eliminated by the addition of an improvement term in the action. Finally we use the Dirac procedure tro obtain solutions for the wave function. This proves that the CGHS theory in two dimensions is quantizable.