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Single Killing Vector Gauss-Bonnet Boson Stars and Single Killing Vector Hairy Black Holes in D>5 Odd DimensionsHenderson, Laura January 2014 (has links)
I construct anti-de Sitter boson stars in Einstein-Gauss-Bonnet gravity coupled to a (D-1)/(2)-tuplet of complex massless scalar field both perturbativelyand numerically in D=5,7,9,11 dimensions. Due to the choice of scalar fields, these solutions possess just a single helical Killing symmetry. For each choice of the Gauss-Bonnet parameter α≠α_cr, the central energy density at the center of the boson star, q_0 completely characterizes the one parameter family of solutions. These solutions obey the first law of thermodynamics, in the case of the numerics, to within 1 part in 10^6. I describe the dependence of the boson star mass, angular momentum and angular velocity on α and on the dimensionality. For α<α_cr and D>5, these quantities exhibit damped oscillations about finite central values and the central energy density tends to infinity. The Kretschmann invariant at the center of the boson star diverges in the limit of diverging central energy. This contrasts the D=5 case, where the Kretschmann invariant diverges at a finite value of the central energy density. Solutions where α<α_cr, correspond to negative mass boson stars, and the for all dimensions the boson star mass and angular momentum decrease exponentially as the central energy density tends toward infinity with the Kretschmann invariant diverging only when in the limit the central energy density diverges.
I also briefly discuss the difficulties of numerically obtaining single Killing vector hairy black hole solutions and present the explicit boundary conditions for both Einstein gravity and Einstein-Gauss-Bonnet gravity.
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Uniformly Area Expanding Flows in SpacetimesXu, Hangjun January 2014 (has links)
<p>The central object of study of this thesis is inverse mean curvature vector flow of two-dimensional surfaces in four-dimensional spacetimes. Being a system of forward-backward parabolic PDEs, inverse mean curvature vector flow equation lacks a general existence theory. Our main contribution is proving that there exist infinitely many spacetimes, not necessarily spherically symmetric or static, that admit smooth global solutions to inverse mean curvature vector flow. Prior to our work, such solutions were only known in spherically symmetric and static spacetimes. The technique used in this thesis might be important to prove the Spacetime Penrose Conjecture, which remains open today. </p><p>Given a spacetime $(N^{4}, \gbar)$ and a spacelike hypersurface $M$. For any closed surface $\Sigma$ embedded in $M$ satisfying some natural conditions, one can ``steer'' the spacetime metric $\gbar$ such that the mean curvature vector field of $\Sigma$ becomes tangential to $M$ while keeping the induced metric on $M$. This can be used to construct more examples of smooth solutions to inverse mean curvature vector flow from smooth solutions to inverse mean curvature flow in a spacelike hypersurface.</p> / Dissertation
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Generalised Robinson-Trautman and Kundt waves and their physical interpretationDocherty, Peter January 2004 (has links)
In this thesis, Newman-Penrose techniques are used to obtain some new exact solutions to Einstein's field equations of general relativity and to assist in the physical interpretation of some exact radiative space-times. Attention is restricted to algebraically special space-times with a twist-free, repeated principal null congruence. In particular, the Robinson-Trautman type N solutions, which describe expanding gravitational waves, are investigated for all possible values of the cosmological constant A and the Gaussian curvature parameter E. The wave surfaces are always (hemi-)spherical, with successive surfaces displaced along time-like, space-like or null lines, depending on E. Explicit sandwich waves of this class are studied in Minkowski, de Sitter or anti-de Sitter backgrounds and a particular family of such solutions, which can be used to represent snapping or decaying cosmic strings, is considered in detail. The singularity and global structure of the solutions is also presented. In the remaining part of the thesis, the complete family of space-times with a non-expanding, shear-free, twist-free, geodesic principal null congruence (Kundt waves), that are of algebraic type III and for which the cosmological constant (Ac) is non-zero, is presented. The possible presence of an aligned pure radiation field is also assumed. These space-times generalise the known vacuum solutions of type N with arbitrary Ac and type III with Ac = O. It is shown that there are two, one and three distinct classes of solutions when Ac is respectively zero, positive and negative and, in these cases, the wave surfaces are plane, spherical or hyperboloidal in Minkowski, de Sitter or anti-de Sitter backgrounds respectively. The singularities which occur in these space-times are interpreted in terms of envelopes of these wave surfaces. Again, by considering functions of the retarded time which "cross-over" between canonical types, sandwich waves are also studied. The limiting cases of these, giving rise to shock or impulsive waves, are also considered.
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Island words, island worlds : the origins and meanings of words for ‘Islands’ in North-West EuropeRonström, Owe January 2009 (has links)
This paper proposes the notion that words mirror ideas, perspectives and worldviews. Etymologies and meanings of general words for ‘islands’ in a number of languagesin North and West Europe are then discussed. Here, islands are shown to be etymologicallyconstituted by the interplay between land and water, and which of these two is emphasizedvaries. In the third section, a number of Swedish island words are surveyed, in an attemptto illuminate the principle of linguistic relativity. Finally, the implications of these findingsfor island studies are discussed.
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Μελέτη των ταλαντώσεων των αστέρων νετρονίων με έμφαση στις ακτινικές ταλαντώσεις τους / A study of the oscillations of the neutron stars with emphasis on their radial oscillationsΚλεφτόγιαννης, Γεώργιος 08 January 2013 (has links)
Στην παρούσα εργασία μελετώνται οι ταλαντώσεις των αστέρων νετρονίων
με ιδιαίτερη έμφαση στις ακτινικές ταλαντώσεις τους. Σκοπός αυτής της μελέτης
είναι ο υπολογισμός των συχνοτήτων των ακτινικών ταλαντώσεων των αστέρων
νετρονίων.
Στο πρώτο, κεφάλαιο κάνουμε μία μικρή εισαγωγή για τους αστέρες νετρονίων
και τους ταχέως περιστρεφόμενους αστέρες νετρονίων (pulsars) καθώς και για
τον ρόλο, που διαδραματίζουν αυτοί και τα διπλά συστήματα που σχηματίζουν,
στην σύγχρονη Αστροφυσική. Ακόμα αναφερόμαστε στην εσωτερική δομή των
αστέρων νετρονίων και σε κάποιες από τις καταστατικές εξισώσεις, που μπορεί
να περιγράφουν την ύλη στο εσωτερικό του, δίνοντας έμφαση στην πολυτροπική
καταστατική εξίσωση την οποία και υιοθετούμε στην παρούσα εργασία.
Στο δεύτερο κεφάλαιο, παραθέτουμε τις εξισώσεις Oppenheimer–Volkoff(OV)
που περιγράφουν την ισορροπία ενός αδιατάρακτου αστέρα νετρονίων. Στη συνέ-
χεια, θεωρώντας τις ακτινικές ταλαντώσεις 1) ως απειροστού πλάτους αδιαβατικές
ταλαντώσεις που διατηρούν τον βαρυονικό αριθμό και 2) ως αποτέλεσμα της
αργής περιστροφής του αστέρα, καταλήγουμε σε μία δεύτερης τάξης διαφορική
εξίσωση που διέπει τις ακτινικές ταλαντώσεις των αστέρων νετρονίων. Η εξί-
σωση αυτή γράφεται στη μορφή Sturm– Liouville. Επιπροσθέτως, συνεχίζουμε
παραθέτοντας τον διορθωτικό όρο, λόγω περιστροφής, για την τιμή της συχνότη-
τας και τις εξισώσεις που διέπουν τις μη ακτινικές ταλαντώσεις. Τέλος κλείνουμε
το κεφάλαιο αυτό με μία ανάλυση των διαφόρων τρόπων ταλάντωσης.
Στο τρίτο κεφάλαιο, αρχικά επιλύουμε, με τη χρήση ενός πρωτότυπου επα-
ναληπτικού αλγορίθμου, το σύστημα διαφορικών εξισώσεων OV για την εύρεση
των φυσικών παραμέτρων του αστέρα. Στη συνέχεια, αφού αρχικά αναλύσουμε
τις βασικότερες μεθόδους επίλυσης της διαφορικής εξίσωσης των ακτινικών ταλα-
ντώσεων, που εμφανίζονται στην βιβλιογραφία, μετατρέπουμε τη μορφή Sturm–
Liouville σε ένα σύστημα δύο διαφορικών εξισώσεων πρώτης τάξης, το οποίο
επιλύουμε με την βοήθεια της μεθόδου σκόπευσης (shooting method).
Στη βιβλιογραφία, υπάρχουν δύο διαφορετικές τάσεις αντιμετώπισης της πο-
λυτροπικής καταστατικής εξίσωσης, ανάλογα με το αν στην θέση της πυκνότητας
εισέρχεται η πυκνότητα μάζας ηρεμίας ή η πυκνότητα της ολικής μάζας–ενέργειας.
Ακόμα, δύο είναι και οι διαφορετικοί τρόποι αντιμετώπισης του αδιαβατικού δεί-
κτη, ο οποίος εισέρχεται στην εξίσωση που περιγράφει τις ακτινικές ταλαντώσεις,
ανάλογα με το αν είναι σταθερός ή μεταβάλλεται. Από τις τέσσερις αυτές βασικές
υποθέσεις για την πολυτροπική καταστατική εξίσωση και τον αδιαβατικό δείκτη,
προκύπτουν τέσσερα διαφορετικά πρωτότυπα μοντέλα για τις ακτινικές ταλαντώ-
σεις, τα οποία και επιλύουμε.
Στο τελευταίο κεφάλαιο, υπολογίζουμε και παρουσιάζουμε τις τρεις πρώτες
συχνότητες των τεσσάρων πρωτότυπων μοντέλων για τις ακτινικές ταλαντώσεις
των αστέρων νετρονίων για τρεις διαφορετικές τιμές του πολυτροπικού δείκτη και
αναλύουμε τις αριθμητικές μεθόδους, τις οποίες χρησιμοποιούμε, καθώς και τις
αντίστοιχες υπορουτίνες της βιβλιοθήκης SLATEC.
Εν κατακλείδι, τα αποτελέσματα αυτής της εργασίας είναι η ανάπτυξη ενός
πρωτότυπου επαναληπτικού αλγορίθμου για την εύρεση της ακτίνας του αστέρα
με μεγάλη ακρίβεια και η παρουσίαση αποτελεσμάτων για τέσσερα πρωτότυπα
μοντέλα που περιγράφουν τις ακτινικές ταλαντώσεις των αστέρων νετρονίων. / In the present Thesis we study the oscillations of neutron stars emphasizing
on the radial oscillations. The Thesis is organized in four chapters. In the first
chapter, we introduce the theoretical background of neutron stars and pulsars. We
then discuss the importance of the role that the binary neutron stars play in modern
Astrophysics. Next, we refer to the structure of these stars and introduce some of
the equations of state (EOS) which try to describe the matter occupying the inner
layers of neutron stars, emphasizing on the polytropic EOS which is adopted here.
In the second chapter we, first introduce the Oppenheimer–Volkoff (OV) system
of differential equations, describing the hydrostatic equilibrium of a non rotating,
non pulsating neutron star, and considering the radial oscillations 1) as infinitesimal,
baryon-number conserving, adiabatic oscillations 2) as the result of the
slow rotation of the neutron star, we derive the second order differential equation
governing the radial oscillations of a neutron star. We then rewrite this equation in
the Sturm–Liouville form. The expression of the change of frequency of the radial
oscillations due to slow rotation and the equations of state is obtained. Finally,
we conclude this chapter with a mode analysis of oscillations of neutron stars in
general.
In the third chapter, we first solve the OV system of differential equations, implementing
an original iterative algorithm, and thus calculate the physical parameters
of the star. Next, some of the methods used for solving the equations describing
the radial oscillations are discussed. Finally, we transform the Sturme–Liouville
form to a set of two first order differential equations, which are computed by implementation
of the shooting method.
In the bibliography, the polytropic EOS is considered in two different ways,
depending on which density (rest mass or total mass–energy) is involved in the
polytropic EOS. In a similar manner, we have two different ways for considering
the adiabatic exponent which enters the equation describing the radial oscillations
(constant or variable). Considering these four different assumptions for the
polytropic EOS and the adiabatic exponent, we construct four different models of
pulsating neutron stars.
In the final chapter, we compute and present the first three frequencies of each
basic model concerning radial oscillations of neutron stars for three values of the
polyropic index. We discuss the numerical methods implemented here and the involved
subroutines, which can be found in the SLATEC Library.
The main issues of the present Thesis are the development of an iterative algorithm
for accurately computing the radius of the star and the computation of the
frequencies for the four basic models describing th radial oscillations of neutron
stars.
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Introdução matemática aos modelos cosmológicosDelbem, Nilton Flávio [UNESP] 15 October 2010 (has links) (PDF)
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delbem_nf_me_rcla.pdf: 885461 bytes, checksum: 9ba35dff1d53b0378c1e134087c575b7 (MD5) / Universidade Estadual Paulista (UNESP) / Esta dissertação tem a proposta de organizar, discutir e apresentar de maneira precisa os conceitos matemáticos de variedade diferenciável e de tensores envolvidos no estudo da Cosmologia sob o ponto de vista da Teoria da Relatividade Geral para o modelo de Friedmann-Lemaître-Robertson-Walker. Busca-se assim apresentar um texto didático que possa ser utilizado tanto nos cursos de graduação em Matemática como de Física para uma disciplina optativa de Introdução Matemática à Cosmologia / The goal of this dissertation is to organize and discuss in a rigorous way the mathematical concepts of manifolds and tensors needed to the study of Cosmology and the Friedmann-Lemaître-Robertson-Walker model under the point of view of the General Relativity. In this way, this dissertation was written as textbook that could be used in an undergraduate course of Physics and Mathematics
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SITUAÇÕES DIDÁTICAS NO ENSINO DA RELATIVIDADE GERAL: ANÁLISE DO ENGAJAMENTO DOS ALUNOS / Didactic Situations in the teaching of General Relativity: analysis of students\' engagementLeticia Zago 04 May 2018 (has links)
Dadas as necessidades da inserção da Física Moderna e Contemporânea no Ensino Médio e a escassez de materiais didáticos que abordem a Relatividade Geral, propomos a construção e aplicação de uma Sequência Didática sobre o tema com o intuito de responder à questão: como os alunos se engajam em atividades propostas a partir de uma Sequência Didática sobre Relatividade no Ensino Médio? A partir das ideias do Engajamento Disciplinar Produtivo (EDP) e pela Teoria das Situações Didáticas, elaboramos uma ferramenta para analisar o engajamento dos alunos nas diferentes interações ocorridas na aula sobre Princípio da Relatividade de Galileu. A partir dos resultados podemos observar a importância das interações ocorridas em torno das situações de validação do conhecimento, nos momentos em que os alunos procuram justificar suas hipóteses e quando a professora realiza a sistematização com base no conhecimento científico, pois revelam progresso intelectual do aluno e, portanto, evidencias de Engajamento Disciplinar Produtivo. Deste modo fica claro a importância do papel das atividades e ações da professora para estimular o uso de mecanismos de prova por parte dos alunos. / Given the needs of the insertion of Modern and Contemporary Physics in High School and the shortage of didactic materials that address General Relativity, we propose the construction and application of a Didactic Sequence on the theme in order to answer the question: How students engage in activities proposed from a Didactic Sequence on Relativity in High School? Based on the ideas of Productive Disciplinary Engagement (DPE) and the Theory of Didactic Situations, we have developed a tool to analyze students\' engagement regarding different interactions that occurred in Galileo Principle of Relativity class. According to the results, we could observe the importance of interactions taken around the validation of knowledge, when the students seek to justify their hypotheses and when the teacher performs the systematization based on scientific knowledge, because they reveal student\'s intellectual progress and, therefore, evidences of Productive Disciplinary Engagement. This makes clear the importance of the role of the teacher\'s activities and actions to stimulate students\' use of proof mechanisms.
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The dynamical approach to relativity as a form of regularity relationalismStevens, Syman January 2014 (has links)
This thesis investigates the interplay between explanatory issues in special relativity and the theory's metaphysical foundations. Special attention is given to the 'dynamical approach' to relativity, promoted primarily by Harvey Brown and collaborators, according to which the symmetries of dynamical laws are explanatory of relativistic effects, inertial motion, and even the Minkowskian geometrical structure of a specially relativistic world. The thesis begins with a review of Einstein's 1905 introduction to special relativity, after which brief historical introductions are given for the standard 'geometrical' approach to relativity and the unorthodox 'dynamical' approach. After a critical review of recent literature on the topic, the dynamical approach is shown to be in need of a metaphysical package that would undergird the explanatory claims mentioned above. It is argued that the dynamical approach is best understood as a form of relationalism - in particular, as a relativistic form of 'regularity relationalism', promoted recently by Nick Huggett. According to this view, some portion of a world's geometrical structure actually supervenes upon the symmetries of the best-system dynamical laws for a material ontology endowed with a primitive sub-metrical structure. To explore the plausibility of this construal of the dynamical approach, a case study is carried out on solutions to the Klein-Gordon equation. Examples are found for which the field values, when purged of all spatiotemporal structure but their induced topology, are still arguably best-systematized by the Klein-Gordon equation itself. This bolsters the plausibility of the claim that some system of field values, endowed with mere sub-metrical structure, might have as its best-systems dynamical laws a (set of) Lorentz-covariant equation(s), on which Minkowski geometrical structure would supervene. The upshot is that the dynamical approach to special relativity can be defended as what might be called an ontologically and ideologically relationalist approach to Minkowski spacetime structure. The chapters refer regularly to three appendices, which include a brief introduction to topological and differentiable spaces.
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Fuzzy BlackholesMurugan, Anand 01 May 2007 (has links)
The fuzzball model of a black hole is an attempt to resolve the many paradoxes and puzzles of black hole physics that have revealed themselves over the last century. These badly behaved solutions of general relativity have given physicists one of the few laboratories to test candidate quantum theories of gravity. Though little is known about exactly what lies beyond the event horizon, and what the ultimate fate of matter that falls in to a black hole is, we know a few intriguing and elegant semi-classical results that have kept physicists occupied. Among these are the known black hole entropy and the Hawking radiation process.
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Um objeto compacto exótico na relatividade geral pseudo-complexaVolkmer, Guilherme Lorenzatto January 2018 (has links)
O impacto que estruturas algébricas podem exercer em teorias físicas e bem ilustrado pela Mecânica Quântica, onde os números complexos são inquestionavelmente a escolha mais adequada para desenvolver a teoria. A Relatividade Geral pseudo-complexa avalia a possibilidade da interação gravitacional assumir sua descrição mais natural quando construída tendo como base os números pseudo-complexos, que consistem em uma das três possibilidades de números complexos abelianos com uma unica unidade imaginária. Esse conjunto numérico e dotado de elementos não nulos cujo produto e zero, tais números recebem o nome de zeros generalizados ou divisores de zero. A presença de zeros generalizados permite a introdução de um princípio variacional modificado do qual um termo adicional, ausente na Relatividade Geral, emerge nas equações de campo. Esse termo adicional e interpretado como uma energia escura, cuja origem física está relacionada com flutuações no vácuo. A inclusão desse efeito e legítima pois flutuações no vácuo a priori devem gravitar como qualquer outra forma de energia. Das equações de campo podemos resumir a principal ideia conceitual da teoria, na Relatividade Geral pseudo-complexa massa não apenas curva o espaçotempo como também e capaz de alterar a estrutura do espaço-tempo ao redor da massa. As diferenças com relação a Relatividade Geral se manifestam em situações físicas extremas, no regime de campos gravitacionais intensos. Como aplicação analisamos sob o ponto de vista teórico um objeto compacto exótico composto por matéria escura fermiônica. / The impact that algebraic structures can exert on physical theories is well illustrated by Quantum Mechanics, where complex numbers are unquestionably the most appropriate choice to develop the theory. Pseudo-complex General Relativity evaluates the possibility that the gravitational interaction acquires its most natural description when constructed upon pseudo-complex numbers, which consist of one of the three possibilities of abelian complex numbers with a single imaginary unit. This numerical set is endowed with nonzero elements whose product is zero, such numbers are called generalized zeros or divisors of zero. The presence of generalized zeros allows the introduction of a modi ed variational principle from which an additional term, absent in General Relativity, emerges in the eld equations. This additional term is interpreted as a dark energy, whose physical origin is related to vacuum uctuations. The inclusion of this e ect is legitimate because a priori vacuum uctuations must gravitate as any other form of energy. From the eld equations we can summarize the main conceptual idea of the theory, in pseudo-complex General Relativity mass not only curves spacetime but also is able to change the structure of the spacetime around the mass. The di erences with respect to General Relativity are manifested in extreme physical situations in the regime of intense gravitational elds. As an application we analyze from the theoretical point of view an exotic compact object composed of fermionic dark matter.
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