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Maidens, Anna Victoria. "The hole argument : substantivalism and determinism in general relativity." Thesis, University of Cambridge, 1993. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.309205.
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Longobardi, Agata. "On the formulation of Einstein general relativity in a phisycal reference system." Doctoral thesis, Universita degli studi di Salerno, 2012. http://hdl.handle.net/10556/347.
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2010 - 2011The research deals with the breaking of the evolution problem of a reversible material system in two different problems, the initial data problem and the restricted evolution problem. This breaking, intrinsically formulated, permits to study of the evolution of a perfect fluid which produces a spherically symmetric 4--manifold. By using different systems of coordinates adapted to the world-lines of this fluid, such as curvature coordinates, gaussian coordinates, gaussian polar coordinates and harmonic coordinates, different exact solutions are obtained. In particular, in gaussian coordinates, I have obtained two solutions already deduced, in a different way, by Wesson and Gutman, showing that they are physically equivalent. In addition, by considering the frames of reference associated to isotropic coordinates and spherical symmetry, I have obtained that the restricted evolution problem gives dynamic models non different from Einstein--deSitter or Friedman--Robertson--Walker or Wyman models; moreover, if the distribution of the fluid is initially regular in the symmetry center, and the Hubble parameter is constant, all the configurations of the fluid are demonstrated to be Euclidean hypersurfaces. Finally, I have studied the geometrical and physical characteristics of the class of reference frames associated to harmonic coordinates. Precisely, I express in relative form the harmonicity conditions and consider the so called “spatially harmonicity" of a reference frame in spherical symmetry. The initial data problem is then analyzed in polar coordinates and the obtained results are applied to special cases of exact solutions. [edited by author]
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Hajj-Boutros, Joseph. "Détermination des nouvelles solutions exactes d’Einstein dans le cas intérieur." Paris 6, 1987. http://www.theses.fr/1987PA066421.
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Ensemble de travaux réalisé dans le cadre de la théorie de la relativité générale. La métrique de l'espace-temps adoptée est à symétrie bien précise pour simplifier dans la mesure du possible les équations du champ d’Einstein. Dans le cadre de la symétrie sphérique statique et non statique, nous avons obtenu de nouvelles solutions des équations du champ (cas intérieur). Dans le cas de la symétrie plane, nous avons pu engendrer plusieurs nouvelles solutions statiques et non statiques. Nous avons mis au point de nouvelles solutions du type cosmologique. L'espace-temps utilise étant essentiellement homogène, nous avons pu étudier le caractère non isotropique de la singularité initiale. Les conditions physiques ont été respectées. Dans le cas des solutions cosmologiques nous avons pu construire un modèle rendant compte de l'évolution possible de notre univers depuis son état initial radiatif et singulier jusqu'à son état actuel. Nous avons trouvé une solution globalement régulière dans le cadre de la symétrie cylindrique. La technique du calcul utilise a consisté dans la plupart des cas à linéariser les équations du champ.
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Ames, Ellery. "Singular Symmetric Hyperbolic Systems and Cosmological Solutions to the Einstein Equations." Thesis, University of Oregon, 2014. http://hdl.handle.net/1794/17905.
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Characterizing the long-time behavior of solutions to the Einstein field equations remains an active area of research today. In certain types of coordinates the Einstein equations form a coupled system of quasilinear wave equations. The investigation of the nature and properties of solutions to these equations lies in the field of geometric analysis. We make several contributions to the study of solution dynamics near singularities. While singularities are known to occur quite generally in solutions to the Einstein equations, the singular behavior of solutions is not well-understood. A valuable tool in this program has been to prove the existence of families of solutions which are so-called asymptotically velocity term dominated (AVTD). It turns out that a method, known as the Fuchsian method, is well-suited to proving the existence of families of such solutions. We formulate and prove a Fuchsian-type theorem for a class of quasilinear hyperbolic partial differential equations and show that the Einstein equations can be formulated as such a Fuchsian system in certain gauges, notably wave gauges. This formulation of Einstein equations provides a convenient general framework with which to study solutions within particular symmetry classes. The theorem mentioned above is applied to the class of solutions with two spatial symmetries -- both in the polarized and in the Gowdy cases -- in order to prove the existence of families of AVTD solutions. In the polarized case we find families of solutions in the smooth and Sobolev regularity classes in the areal gauge. In the Gowdy case we find a family of wave gauges, which contain the areal gauge, such that there exists a family of smooth AVTD solutions in each gauge.
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Stark, Elizabeth. "Gravitoelectromagnetism and the question of stability in general relativity." Monash University, School of Mathematical Sciences, 2004. http://arrow.monash.edu.au/hdl/1959.1/9509.
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Taylor, Stephen M. "On Stability and Evolution of Solutions in General Relativity." Diss., CLICK HERE for online access, 2007. http://contentdm.lib.byu.edu/ETD/image/etd2033.pdf.
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Dilts, James. "The Einstein Constraint Equations on Asymptotically Euclidean Manifolds." Thesis, University of Oregon, 2015. http://hdl.handle.net/1794/19237.
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In this dissertation, we prove a number of results regarding the conformal method of finding solutions to the Einstein constraint equations. These results include necessary and sufficient conditions for the Lichnerowicz equation to have solutions, global supersolutions which guarantee solutions to the conformal constraint equations for near-constant-mean-curvature (near-CMC) data as well as for far-from-CMC data, a proof of the limit equation criterion in the near-CMC case, as well as a model problem on the relationship between the asymptotic constants of solutions and the ADM mass. We also prove a characterization of the Yamabe classes on asymptotically Euclidean manifolds and resolve the (conformally) prescribed scalar curvature problem on asymptotically Euclidean manifolds for the case of nonpositive scalar curvatures.
This dissertation includes previously published coauthored material.
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Gasperin, Garcia. "Applications of conformal methods to the analysis of global properties of solutions to the Einstein field equations." Thesis, Queen Mary, University of London, 2017. http://qmro.qmul.ac.uk/xmlui/handle/123456789/25820.
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Although the study of the initial value problem in General Relativity started in the decade of 1950 with the work of Foures-Bruhat, addressing the problem of global non-linear stability of solutions to the Einstein field equations is in general a hard problem. The first non-linear global stability result in General Relativity was obtained for the de-Sitter spacetime by means of the so-called conformal Einstein field equations introduced by H. Friedrich in the decade of 1980. The latter constitutes the main conceptual and technical tool for the results discussed in this thesis. In Chapter 1 the physical and geometrical motivation for these equations is discussed. In Chapter 2 the conformal Einstein equations are presented and first order hyperbolic reduction strategies are discussed. Chapter 3 contains the first result of this work; a second order hyperbolic reduction of the spinorial formulation of the conformal Einstein field equations. Chapter 4 makes use of the latter equations to give a discussion of the non-linear stability of the Milne universe. Chapter 5 is devoted to the analysis of perturbations of the Schwarzschild-de Sitter spacetime via suitably posed asymptotic initial value problems. Chapter 6 gives a partial generalisation of the results of Chapter 5. Finally a result relating the Newman-Penrose constants at future and past null infinity for spin-1 and spin-2 fields propagating on Minkowski spacetime close to spatial infinity is discussed in Chapter 7 exploiting the framework of the cylinder at spatial in nity. Collectively, these results show how the conformal Einstein field equations and more generally conformal methods can be employed for analysing perturbations of spacetimes of interest and extract information about their conformal structure.
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Machado, Ramos Maria da Peidade. "Invariant differential operators and the equivalence problem of algebraically special spacetimes." Thesis, University of Southampton, 1996. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.241986.
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Bredberg, Irene. "The Einstein and the Navier-Stokes Equations: Connecting the Two." Thesis, Harvard University, 2012. http://dissertations.umi.com/gsas.harvard:10214.
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This thesis establishes a precise mathematical connection between the Einstein equations of general relativity and the incompressible Navier-Stokes equation of fluid dynamics. We carry out a holographic analysis which relates solutions to the Einstein equations to the behaviour of a dual fluid living in one fewer dimensions. Gravitational systems are found to exhibit Navier-Stokes behaviour when we study the dynamics of the region near an event horizon. Thus, we find non-linear deformations of Einstein solutions which, after taking a suitable near horizon limit and imposing our particular choice of boundary conditions, turn out to be precisely characterised by solutions to the incompressible Navier-Stokes equation. In other words, for any solution to the Navier-Stokes equation, the set-up we present provides a solution to the Einstein equations near a horizon. We consider the cases of fluids flowing on the plane and on the sphere. Fluid dynamics on the plane is analysed foremost in the context of a flat background geometry whilst the spherical analysis is undertaken for Schwarzschild black holes and the static patch of four-dimensional de Sitter space.Physics
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Van, der Walt Petrus Johannes. "Numerical relativity on cosmological past null cones." Thesis, Rhodes University, 2013. http://hdl.handle.net/10962/d1002959.
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The observational approach to cosmology is the endeavour to reconstruct the geometry of the Universe using only data that is theoretically verifiable within the causal boundaries of a cosmological observer. Using this approach, it was shown in [36] that given ideal cosmological observations, the only essential assumption necessary to determine the geometry of the Universe is a theory of gravity. Assuming General Relativity, the full set of Einstein field equations (EFEs) can be used to reconstruct the geometry of the Universe using direct observations on the past null cone (PNC) as initial conditions. Observationally and theoretically this is a very ambitious task and therefore, current developments have been restricted to spherically symmetric dust models while only relaxing the usual assumption of homogeneity in the radial direction. These restricted models are important for the development of theoretical foundations and also useful as verification models since they avoid the circularity of verifying what has already been assumed. The work presented in this thesis is the development of such a model where numerical relativity (NR) is used to simulate the observable universe. Similar to the work of Ellis and co-workers [36], a reference frame based on the PNC is used. The reference frame used here, however, is based on that of the characteristic formalism of NR, which has developed for calculating the propagation of gravitational waves. This provides a formalism that is well established in NR, making the use of existing algorithms possible. The Bondi-Sachs coordinates of the characteristic formalism is, however, not suitable for calculations beyond the observer apparent horizon (AH) since the diameter distance used as a radial coordinate becomes multi-valued when the cosmological PNC reconverges in the history of a universe, smaller in the past. With this taken into consideration, the Bondi-Sachs characteristic formalism is implemented for cosmology and the problem approaching the AH is investigated. Further developments address the limitations approaching the AH by introducing a metric based on the Bondi-Sachs metric where the radial coordinate is replaced with an affine parameter. The model is derived with a cosmological constant Λ incorporated into the EFEs where Λ is taken as a parameter of the theory of gravity rather than as a matter source term. Similar to the conventional characteristic formalism, this model consists of a system of differential equations for numerically evolving the EFEs as a characteristic initial value problem (CIVP). A numerical code implemented for the method has been found to be second order convergent. This code enables simulations of different models given identical data on the initial null cone and provides a method to investigate their physical consistency within the causally connected region of our current PNC. These developments closely follow existing 3D schemes developed for gravitational wave simulations, which should make it natural to extend the affine CIVP beyond spherical symmetric simulations. The developments presented in this thesis is an extended version of two papers published earlier.
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Godazgar, Mohammad Mahdi. "Aspects of higher dimensional Einstein theory and M-theory." Thesis, University of Cambridge, 2012. https://www.repository.cam.ac.uk/handle/1810/245148.
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This thesis contains two main themes. The first is Einstein's theory of general relativity in higher dimensions, while the second is M-theory. The first part of the thesis concerns the use of classification techniques based on the Weyl curvature in an attempt to systematically study higher dimensional general relativity and its solutions. After a review of the various classification schemes, the application of these schemes to the study of higher dimensional solutions is explained. The first application of the tensor approach that is discussed is the systematic classification of higher dimensional axisymmetric solutions. A complete classification of all algebraically special axisymmetric solutions to the vacuum Einstein equation in higher dimensions is presented. Next, the study of perturbations of higher dimensional solutions within this framework and the possibility of decoupling equations for black hole solutions of interest, as has been successfully done in four dimensions, is considered. In the case where such a decoupling of the perturbations is possible, a map for constructing solutions of the perturbation equation is presented and is applied to the Kerr/CFT correspondence. Also, the property of gravitational radiation emitted from an isolated source in higher dimensions is considered and the tensor classification scheme is used to derive the peeling property of the Weyl tensor in higher dimensions. This is shown to be different to that which occurs in four dimensions. Finally, after an in-depth exposition of the spinor classification scheme and its relation to the tensor approach, solutions belonging to the most special type in the spinor classification are classified. In addition, the classification of the black ring in this scheme is discussed. The second part of the thesis explores the use of generalised geometry as a tool for better understanding M-theory. After briefly reviewing the curious phenomenon of M-theory dualities, it is explained how generalised geometry can be used to show that these symmetries are not exclusive to compactifications of the theory, but can be made manifest without recourse to compactification. Finally, results regarding the local symmetries of M-theory in the generalised geometry framework for a particular symmetry group are presented.
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Dengiz, Suat. "3+1 Orthogonal And Conformal Decomposition Of The Einstein Equation And The Adm Formalism For General Relativity." Master's thesis, METU, 2011. http://etd.lib.metu.edu.tr/upload/12612949/index.pdf.
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In this work, two particular orthogonal and conformal decompositions of the 3+1 dimensional Einstein equation and Arnowitt-Deser-Misner (ADM) formalism for general relativity are obtained. In order to do these, the 3+1 foliation of the four-dimensional spacetime, the fundamental conformal transformations and the Hamiltonian form of general relativity that leads to the ADM formalism, de
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Lukács, Orsolya. "C.G. Jung and Albert Einstein : from the physical to the psychical relativity of space and time." Thesis, University of Essex, 2018. http://repository.essex.ac.uk/22134/.
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Despite Carl Gustav Jung’s acknowledgement of Albert Einstein’s influence on his thinking, and despite the significant number of studies into Jung’s interest in physics – and his collaboration with the theoretical physicist Wolfgang Pauli – so far there has been no thorough investigation into the connection between Jung and Einstein. This thesis researches the historical context of the relationship between Jung and Einstein, and the extent of Einstein’s influence on Jung’s concepts and system of psychology, and thereby redresses the balance of the theoretical argument about the intellectual influences on Jung from the field of physics. First, it explores the dynamics and importance of the relationship between the two men, and reconstructs the narrative of this connection. It identifies other key figures who played a mediating role between Jung and Einstein and investigates their involvement in conveying Einstein’s special and general theories of relativity to Jung as well as their part in the formation and subsequent deterioration of the relationship between Jung and Einstein. Secondly, this thesis analyses Einstein’s influence on Jung's reconceptualization of libido as psychic energy, and Jung’s employment of the theory of relativity in his writings, which culminates in his conception of the ‘psychic relativity of space and time’, the idea that underpins his theory of synchronicity.
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Canonico, Rosangela. "Exact solutions in general relativity and alternative theories of gravity: mathematical and physical properties." Doctoral thesis, Universita degli studi di Salerno, 2011. http://hdl.handle.net/10556/181.
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2009 - 2010In this thesis, we discuss several subjects connected with the framework of GR, in order to characterize astrophysical compact objects. The main purpose is to provide simple models describing gravitational fields generated by isolated compact bodies in stationary rotation with extremely simple internal structure, such as neutron stars. The main tools used for our analysis are exact solutions of Einstein fields equations, which have been approached in different ways. In particular, we use the formalism of junction conditions for finding new solutions of Einstein equations in presence of matter by matching metrics representing two shells of a compact body. With the same aim, we introduce the Newmann-Janis Algorithm, a solution generating technique which provides metrics of reduced symmetries from symmetric ones. Finally, an exact solution of Einstein's field equations, known as Einstein Static Universe is studied in the framework of Cosmology. Our purpose is to study the stability properties of this solution focusing on the intriguing possibility of finding static solutions in open cosmological models (k = -1). [edited by author]
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Santos, Calebe Martes de Andrade. "Equações diferenciais e a equação de campo de Einstein." Universidade Federal de Goiás, 2018. http://repositorio.bc.ufg.br/tede/handle/tede/8250.
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This work has as main objective, besides exposing some techniques of solving differential equations of first and second order, to find solutions to Einstein Field Equation, through these techniques. The work was divided in 3 parts, being them, introduction and two other chapters. In the introduction, we tell a bit about the history of differential equations, as well as covering some important passages in the history of General Theory of Relativity. In the first chapter, in a preliminary way, a study was made on some differential equations of first and second orders. The second chapter refers to the application of second-order differential equations as a solution to Einstein's Field Equation. In this last chapter, we have done a study on the article Invariant solutions for the static vacuum equation and we present some other solutions to Einstein's Field Equation. For the writing of the work, a bibliographical revision was made in relation to the subjects addressed in it, thus relating the ideas and definitions of some authors throughout the text.
Este trabalho tem como principal objetivo, além de expôr algumas técnicas de resolução de equações diferenciais de primeira e segunda ordens, encontrar soluções para Equação de Campo de Einstein, através dessas técnicas. O trabalho foi dividido em 3 partes, sendo elas, introdução e mais dois capítulos. Na introdução, contamos um pouco da história das equações diferenciais, além de abordarmos alguns trechos importantes da história da Teoria da relatividade geral. No primeiro capítulo, de forma preliminar, foi feito um estudo sobre algumas equações diferenciais de primeira e segunda ordens. O segundo capítulo, refere-se à aplicação de equações diferenciais de segunda ordem como solução para Equação de Campo de Einstein. Neste último capítulo, fizemos um estudo sobre o artigo Invariant solutions for the static vacuum equation e expomos algumas outras soluções para Equação de Campo de Einstein. Para a escrita do trabalho, foi feita uma revisão bibliográfica em relação aos assuntos abordados no mesmo, relacionando assim, as ideias e definições de alguns autores no decorrer do texto.
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Ahlqvist, Pontus. "Modified Einstein Hilbert Action and the Resulting Field Equations." Honors in the Major Thesis, University of Central Florida, 2007. http://digital.library.ucf.edu/cdm/ref/collection/ETH/id/1016.
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This item is only available in print in the UCF Libraries. If this is your Honors Thesis, you can help us make it available online for use by researchers around the world by following the instructions on the distribution consent form at http://library.ucf.edu/Systems/DigitalInitiatives/DigitalCollections/InternetDistributionConsentAgreementForm.pdf You may also contact the project coordinator, Kerri Bottorff, at kerri.bottorff@ucf.edu for more information.Bachelors
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Daher, Ivo Martins. "Soluções das equações de campo de Einstein para fluidos perfeitos estáticos com simetria esférica." Universidade do Estado do Rio de Janeiro, 2008. http://www.bdtd.uerj.br/tde_busca/arquivo.php?codArquivo=1012.
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Coordenação de Aperfeiçoamento de Pessoal de Nível SuperiorNesta dissertação, procuramos soluções exatas das equações de campo de Einstein em Relatividade Geral que descrevem um fluido perfeito em um espaço-tempo estático com simetria esférica. A técnica utilizada para encontrar essas soluções é o algoritmo de Kovacic, que pode ser aplicado a equações diferenciais ordinárias lineares e homogêneas de segunda ordem com coeficientes racionais. Esse algoritmo é capaz de nos dar soluções fechadas em termos de funções liouvillianas, se tal equação tiver esse tipo de solução. Para esse fim, vários sistemas de coordenadas foram investigados até encontrar o que fosse mais adequado à aplicação do algoritmo. Impondo que a função da métrica 11 g seja racional, ficamos com uma equação diferencial linear e homogênea de segunda ordem que tem coeficientes racionais. Nesse trabalho, as formas arbitradas foram: g11=-A/4x x-z1/x-Z1, g11=-A/4x x-z1/(x-Z1)(x-Z2), g11=-A/4x (x-z1) (x-z2)/x-Z1 e g11= -A/4x (x-z1) (x-z2)/ 4x(x-Z1) (x-Z2) onde x é uma coordenada espacial da métrica e Α, z1 , z2 , Z1 e Z2 são parâmetros dos modelos. Depois de obter soluções analíticas, verificamos se elas satisfazem determinadas condições físicas e, então, poderiam ser utilizadas como modelos de estrelas de nêutrons sem rotação (estrelas de alta densidade).
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Dold, Dominic Nicolas. "Instabilities in asymptotically AdS spacetimes." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/273930.
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In recent years, more and more efforts have been expended on the study of $n$-dimensional asymptotically anti-de Sitter spacetimes $(\mathcal{M},g)$ as solutions to the Einstein vacuum equations \begin{align*} \mathrm{Ric}(g)=\frac{2}{n-2}\Lambda\, g \end{align*} with negative cosmological constant $\Lambda$. This has been motivated mainly by the conjectured instability of these solutions. The author of this thesis joins these efforts with two contributions, which are themselves independent of each other. In the first part, we are concerned with a superradiant instability for $n=4$. For any cosmological constant $\Lambda=-3/\ell^2$ and any $\alpha < 9/4$, we find a Kerr-AdS spacetime $(\mathcal{M},g_{\mathrm{KAdS}})$, in which the Klein-Gordon equation \begin{align*} \Box_g\psi+\frac{\alpha}{\ell^2}\psi=0 \end{align*} has an exponentially growing mode solution satisfying a Dirichlet boundary condition at infinity. The spacetime violates the Hawking-Reall bound $r_+^2 > |a|\ell$. We obtain an analogous result for Neumann boundary conditions if $5/4 < \alpha < 9/4$. Moreover, in the Dirichlet case, one can prove that, for any Kerr-AdS spacetime violating the Hawking-Reall bound, there exists an open family of masses $\alpha$ such that the corresponding Klein-Gordon equation permits exponentially growing mode solutions. Our result provides the first rigorous construction of a superradiant instability for a negative cosmological constant. In the second part, we study perturbations of five-dimensional Eguchi-Hanson-AdS spacetimes exhibiting biaxial Bianchi IX symmetry. Within this symmetry class, the Einstein vacuum equations are equivalent to a system of non-linear partial differential equations for the radius $r$ of the spheres, the Hawking mass $m$ and $B$, a quantity measuring the squashing of the spheres, which satisfies a non-linear wave equation. First we prove that the system is well-posed as an initial-boundary value problem around infinity $\mathcal{I}$ with $B$ satisfying a Dirichlet boundary condition. Second, we show that initial data in the biaxial Bianchi IX symmetry class around Eguchi-Hanson-AdS spacetimes cannot form horizons in the dynamical evolution.
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Gabel, Oliver [Verfasser], Reinhold [Akademischer Betreuer] Walser, and Gernot [Akademischer Betreuer] Alber. "Bose-Einstein Condensates in Curved Space-Time – From Concepts of General Relativity to Tidal Corrections for Quantum Gases in Local Frames / Oliver Gabel ; Reinhold Walser, Gernot Alber." Darmstadt : Universitäts- und Landesbibliothek Darmstadt, 2019. http://d-nb.info/1196294836/34.
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Lawrence, Miles D. "Einstein's Equations in Vacuum Spacetimes with Two Spacelinke Killing Vectors Using Affine Projection Tensor Geometry." VCU Scholars Compass, 1994. http://scholarscompass.vcu.edu/etd/1473.
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Einstein's equations in vacuum spacetimes with two spacelike killing vectors are explored using affine projection tensor geometry. By doing a semi-conformal transformation on the metric, a new "fiducial" geometry is constructed using a projection tensor fields. This fiducial geometry provides coordinate independent information about the underlying structure of the spacetime without the use of an explicit form of the metric tensor.
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Julié, Félix-Louis. "Sur le problème à deux corps et le rayonnement gravitationnel en théories scalaire-tenseur et Einstein-Maxwell-dilaton." Thesis, Sorbonne Paris Cité, 2018. http://www.theses.fr/2018USPCC131/document.
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Avec la naissance de l’"astronomie gravitationnelle", vient l’opportunité inédite de tester la relativité générale et ses alternatives dans un régime de champ fort jamais observé jusqu’alors : celui de la coalescence d’un système binaire d’objets compacts. Cette thèse propose d’étudier le problème du mouvement ainsi que du rayonnement gravitationnel d’un tel système en gravités modifiées, en y adaptant et en généralisant certains développements analytiques clés de la relativité générale. On montre d’abord comment étendre le formalisme "effective-one-body" (EOB) à une large classe de gravités modifiées, parmi lesquelles les théories scalaire-tenseur. Dans ces dernières, l’interaction gravitationnelle est modifiée par l’ajout d’un degré de liberté scalaire (sans masse) à la relativité générale. Le lagrangien à deux corps correspondant étant connu à l’ordre post-post-keplerien, nous construisons un hamiltonien EOB associé, décrivant le mouvement d’une particule test dans des champs effectifs. Ceci permet de simplifier la dynamique à deux corps et d’en définir une resommation ; et ainsi, d’en explorer le régime de champ fort, près de la coalescence du système. On "s’attaque" ensuite, et pour la première fois, à la description analytique d’un système binaire de trous noirs "chevelus", afin d’obtenir les formes d’ondes gravitationnelles (EOB) associées ; et ce, sur l’exemple simple des théories Einstein-Maxwell-dilaton, qui généralisent les théories scalaire-tenseur par l’ajout d’un champ vectoriel (sans masse). Pour ce faire, on calcule le lagrangien à deux corps à l’ordre post-keplerien ainsi que le flux d’énergie rayonnée à l’infini à l’ordre quadrupolaire. Tout comme en relativité générale, ces développements reposent sur la description de la trajectoire des trous noirs par les lignes d’univers de particules ponctuelles, décrites par une action "skeleton" généralisant celle, géodésique, de la relativité générale. Enfin, à l’aide des "superpotentiels" de Katz, que l’on généralise pour définir la masse (nœtherienne) d’un trou noir à "cheveux" vectoriel et scalaire, on montre que la première loi de la thermodynamique qui en découle est particulièrement adaptée, lorsqu’un trou noir est membre d’un système binaire, pour en décrire les réajustements éventuels sous l’influence d’un compagnon lointain. La thermodynamique des trous noirs est alors utilisée pour interpréter et discuter du domaine de validité de leur "skeletonisation"With the birth of "gravitational wave astronomy" comes the opportunity to test general relativity and its alternatives in a strong field regime that had never been observed so far: that of the coalescence of a compact binary sytem. This thesis studies the problem of motion and gravitational radiation from such systems in modified gravities, by adapting some of the key analytical tools that were first developed in the context of general relativity. First, we show how to widen the "effective-one-body" (EOB) formalism to a large class of modified gravities, including, e.g., scalar-tensor theories. In the latter, the gravitational interaction is described by supplementing general relativity with a (massless) scalar degree of freedom. The corresponding two-body lagrangian being known at post-post-keplerian order, we build an associated EOB hamiltonian, which describes the motion of a test particle orbiting in effective external fields. This enables to simplify and resum the two-body dynamics; and hence, to explore the strong-field regime near merger. We then "tackle", for the first time, the analytical description of "hairy" binary black hole systems, and obtain their (EOB) gravitational waveform counterparts in Einstein-Maxwell-dilaton theories, which generalize scalar-tensor theories by means of a (massless) vector field. To that end, we derive the two-body lagrangian at post-keplerian order as well as the energy flux radiated at infinity at quadrupolar order. As in general relativity, our developments rely on the phenomenological description of the black hole’s trajectories as worldlines of point particles that are, in turn, described by a "skeleton" action generalizing that of general relativity. Finally, we develop a formalism based on Katz’ "superpotentials" to define the mass (as a nœther charge) of a black hole that is endowed with vector and scalar "hair". We then deduce the first law of thermodynamics, which is particularly suitable to describe its readjustments when interacting with a faraway companion. Black hole thermodynamics is lastly shown to be a powerful tool to interpret and discuss the scope of their "skeletonization"
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Cattoën, Céline. "Applied mathematics of space-time & space+time : problems in general relativity and cosmology : a thesis submitted to the Victoria University of Wellington in fulfilment of the requirements for the degree of Doctor of Philosophy in Mathematics /." ResearchArchive@Victoria e-thesis, 2009. http://hdl.handle.net/10063/972.
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Dominguez, Angel David Masa. "Buracos negros regulares e outros objetos compactos eletricamente carregados." reponame:Repositório Institucional da UFABC, 2017.
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Orientador: Prof. Dr. Vilson Tonin ZanchinDissertação (mestrado) - Universidade Federal do ABC, Programa de Pós-Graduação em Física, 2017.
No presente trabalho estudam-se buracos negros regulares e outros objetos compactos eletricamente carregados no contexto das teorias de Einstein-Maxwell. O objetivo principal do trabalho é a construção de soluções de buracos negros regulares e o estudo da estabilidade de cada solução. Com tal propósito, primeiro revisamos alguns conceitos fundamentais da Relatividade Geral e apresentamos as equações principais a serem usadas. Em particular, escrevemos explicitamente as equações de campo de Einstein para o caso de um uido anisotrópico eletricamente carregado, cuja distribuição de matéria-energia tem simetria esférica e uma equação de estado do tipo de Sitter, onde a pressão radial é igual ao negativo da densidade de energia. Em seguida, a equação de campo de Einstein é usada para busca de duas soluções, uma solução interior para a região com matéria, a qual não apresente singularidade, e outra solução exterior para a região fora da matéria que corresponde à métrica de Reissner-Nordström. Para construir uma solução à equação de campo de Einstein que seja válida em todos os pontos do espaço, aplicamos o formalismo de junção de Darmois-Israel com uma thin shell tipo-tempo. Supõe-se que a thin shell pode ter massa (densidade de energia) e pressão, na forma de um uido perfeito que obedece uma equação de estado barotrópica P = !. Uma equação de movimento para a shell é derivada das condições de junção. Encontram-se soluções estacionárias de buracos negros regulares e outros objetos compactos eletricamente carregados para escolhas especicas do parâmetro !, e encontram-se as regiões de estabilidade da solução para os casos em que a massa própria da shell é não negativa.
In the present work we study black holes and other electrically charged compact objects in the context of the Einstein-Maxwell theory. The main objective is the construction of solutions of black holes and the study of their stability. With this purpose, we rst reviewed some fundamental concepts of General Relativity introducing the main equations to be used. In particular, we write explicitly the Einstein's eld equations for the case of an electrically charged anisotropic uid, which presents spherical symmetry and a de Sitter type equation of state, where the radial pressure is equal to the negative of energy density. Then, the Einstein eld equation is used to search for two solutions, an interior solution for the region with matter, which presents no singularity, and an external solution for the region outside the matter, that corresponds to the Reissner-Nordström metric. To construct a complete solution we apply the Darmois-Israel junction conditions with a timelike thin shell at the matching surface. It is assumed that the thin shell may have mass (energy density) and pressure, in the form of a perfect uid obeying the barotropic equation of state P = !. The equations of motion for the shell is derived from the junction conditions. We show that there are stationary electrically charged regular black holes solutions and other compact objects for specic choices of the ! parameter. We also show the stability and instability regions of the solutions considering the regions fo the parameter space for which the the mass of the shell is non-negative.
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Civin, Damon. "Stability of charged rotating black holes for linear scalar perturbations." Thesis, University of Cambridge, 2015. https://www.repository.cam.ac.uk/handle/1810/247397.
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In this thesis, the stability of the family of subextremal Kerr-Newman space- times is studied in the case of linear scalar perturbations. That is, nondegenerate energy bounds (NEB) and integrated local energy decay (ILED) results are proved for solutions of the wave equation on the domain of outer communications. The main obstacles to the proof of these results are superradiance, trapping and their interaction. These difficulties are surmounted by localising solutions of the wave equation in phase space and applying the vector field method. Miraculously, as in the Kerr case, superradiance and trapping occur in disjoint regions of phase space and can be dealt with individually. Trapping is a high frequency obstruction to the proof whereas superradiance occurs at both high and low frequencies. The construction of energy currents for superradiant frequencies gives rise to an unfavourable boundary term. In the high frequency regime, this boundary term is controlled by exploiting the presence of a large parameter. For low superradiant frequencies, no such parameter is available. This difficulty is overcome by proving quantitative versions of mode stability type results. The mode stability result on the real axis is then applied to prove integrated local energy decay for solutions of the wave equation restricted to a bounded frequency regime. The (ILED) statement is necessarily degenerate due to the trapping effect. This implies that a nondegenerate (ILED) statement must lose differentiability. If one uses an (ILED) result that loses differentiability to prove (NEB), this loss is passed onto the (NEB) statement as well. Here, the geometry of the subextremal Kerr-Newman background is exploited to obtain the (NEB) statement directly from the degenerate (ILED) with no loss of differentiability.
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Busch, Xavier. "Effets dispersifs et dissipatifs en théorie quantique des champs en espace-temps courbe pour modéliser des systèmes de matière condensée." Thesis, Paris 11, 2014. http://www.theses.fr/2014PA112205/document.
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Les deux principales prédictions de la théorie quantique des champs en espace-temps courbe, à savoir la radiation de Hawking et la production de paires de particules ayant lieu dans un espace-temps non stationnaire, n'ont jamais été testé expérimentalement et impliquent toutes deux des processus à ultra haute énergie. En conséquence, de telles prédictions doivent être considérées prudemment. En utilisant l'analogie avec des systèmes de matière condensée mise en avant par Unruh, leur analogue pourrait être testé en laboratoire. Par ailleurs, dispersion et dissipation sont toujours présentes dans de tels systèmes, ce qui régularise la théorie à courte distances. Lors d'expériences destinées à tester les prédictions citées ci-dessus, le bruit thermique modifiera le résultat. En effet, il existe une compétition entre l'émission stimulée dudit bruit thermique et l'émission spontanée issue du vide quantique. Afin de mesurer la radiation de Hawking analogue et de l'analogue des productions de paires (souvent appelé effet Casimir dynamique), il est alors nécessaire de calculer les conséquence de la dispersion et de la dissipation, ainsi que d'identifier des observables permettant de certifier que l'amission spontanée a eu lieu. Dans cette thèse, nous analyserons d'abord les effets de la dispersion et de la dissipation à la fois sur la radiation de Hawking et sur la production de paires de particules. Afin d'obtenir des résultats explicites, nous travaillerons avec l'espace-temps de de Sitter. Les symétries de la théorie nous permettront d'obtenir des résultats exacts. Ceux-ci seront alors appliqués aux trous noirs grâce aux ressemblances entre la région proche du trou noir et l'espace de de Sitter. Afin d’introduire de la dissipation, nous considérerons un modèle exactement soluble permettant de modéliser n'importe quel taux de dissipation. Dans un tel modèle, le champ est couplé de manière linéaire à un environnement contenant un ensemble dense de degrés de liberté. Dans un tel contexte, nous étudierons l'intrication des particules produites. Ensuite, nous considérerons des systèmes de matière condensée spécifiques, à savoir les condensats de Bose et les polaritons. Nous analyserons les effets de la dissipation sur l'intrication de l’effet Casimir dynamique. Enfin, nous étudieront de manière générique l'intrication de la radiation de Hawking en présence de dispersion pour des systèmes analoguesThe two main predictions of quantum field theory in curved space-time, namely Hawking radiation and cosmological pair production, have not been directly tested and involve ultra high energy configurations. As a consequence, they should be considered with caution. Using the analogy with condensed matter systems put forward by Unruh, their analogue versions could be tested in the lab. Moreover, the high energy behavior of these systems is known and involved dispersion and dissipation, which regulate the theory at short distances. When considering experiments which aim to test the above predictions, the thermal noise will contaminate the outcome. Indeed, there will be a competition between the stimulated emission from thermal noise and the spontaneous emission out of vacuum. In order to measure the quantum analogue Hawking radiation, or the analogue pair production also called dynamical Casimir effect, one should thus compute the consequences of ultraviolet dispersion and dissipation, and identify observables able to establish that the spontaneous emission took place. In this thesis, we first analyze the effects of dispersion and dissipation on both Hawking radiation and pair particle production. To get explicit results, we work in the context of de Sitter space. Using the extended symmetries of the theory in such a background, exact results are obtained. These are then transposed to the context of black holes using the correspondence between de Sitter space and the black hole near horizon region. To introduce dissipation, we consider an exactly solvable model producing any decay rate. In such a model, the field is linearly coupled to an environment containing a dense set of degrees of freedom. We also study the quantum entanglement of the particles so produced. In a second part, we consider explicit condensed matter systems, namely Bose Einstein condensates and exciton-polariton systems. We analyze the effects of dissipation on entanglement produced by the dynamical Casimir effect. As a final step, we study the entanglement of Hawking radiation in the presence of dispersion for a generic analogue system
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Messenger, Paul Henry. "Rotating perfect fluid bodies in Einstein's general theory of relativity." Thesis, University of South Wales, 2005. https://pure.southwales.ac.uk/en/studentthesis/rotating-perfect-fluid-bodies-in-einsteins-general-theory-of-relativity(127bc15d-ff0d-4f8e-80fe-351c24273697).html.
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The study of rotating astrophysical bodies is of great importance in understanding the structure and development of the Universe. Rotating bodies, are not only of great interest in their own right, for example pulsars, but they have also been targeted as prime possible sources of gravitational waves, currently a topic of great interest. The ability of general relativity to describe the laws and phenomena of the Universe is unparalleled, but however there has been little success in the description of rotating astrophysical bodies. This is not due to a lack of interest, but rather the sheer complexity of the mathematics. The problem of the complexity may be eased by the adoption of a perturbation technique, in that a spherically symmetric non-rotating fluid sphere described by Einstein's equations is endowed with rotation, albeit slowly, and the result is expressed and analysed using Taylor's series. A further consideration is that of the exterior gravitational field, which must be asymptotically flat. It has been shown from experiment that, in line with the prediction of general relativity, a rotating body does indeed drag space-time around with it. This leads to the conclusion that the exterior gravity field must not only be asymptotically flat, but must also rotate. The only vacuum solution to satisfy these conditions is the Kerr metric. This work seeks to show that an internal rotating perfect fluid source may be matched to the rotating exterior Kerr metric using a perturbation technique up to and including second order parameters in angular velocity. The equations derived, are used as a starting point in the construction of such a perfect fluid solution, and it is shown how the method may be adapted for computer implementation.
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Borghini, Stefano. "On the characterization of static spacetimes with positive cosmological constant." Doctoral thesis, Scuola Normale Superiore, 2018. http://hdl.handle.net/11384/85730.
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In this thesis we study static vacuum spacetimes. These are very special solutions
of the Einstein Field Equations in General Relativity, where the Lorentzian
structure disappears and we are left with the study of a system of PDEs on
a Riemannian manifold. Although they represent the simplest examples of
spacetimes, their study is by no means trivial. Our main focus will be on spacetimes
with positive cosmological constant, even though we will provide a general
overview of the other cases as well.
Our main contribution is the introduction of a new notion of mass (which will
be called virtual mass) on vacuum static spacetimes with positive cosmological
constant. We will show the plausibility of our definition, by proving that the
virtual mass satisfies properties analogous to the well known Positive Mass
Theorem and Riemannian Penrose Inequality for Riemannian manifolds with
nonnegative scalar curvature.
As a consequence, we will prove a uniqueness theorem for the Schwarzschild–
de Sitter spacetime. As we will discuss, this result shares some similarities
with the well known Black Hole Uniqueness Theorem for the Schwarzschild
spacetime.
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Menadeo, Nicola. "Formalismo 3+1 ed approccio hamiltoniano alla relatività generale." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14602/.
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Nel primo capitolo di questo elaborato verranno descritti ed analizzati alcuni concetti di base della geometria differenziale generalizzandoli a spazi a dimensione arbitraria, per poi utilizzarli nel caso specifico dello spazio-tempo quadridimensionale in cui opera la relatività generale. Verrà fatto largo uso della nozione di ipersuperficie, fondamentale per l'approccio matematico al formalismo 3+1 e verrà studiato il modo in cui questa evolve, da cui segue il concetto di foliazione dello spazio-tempo.
Lo scopo finale sarà quello di decomporre i tensori di Riemann e Ricci che giocano un ruolo centrale nella equazione di campo di Einstein.
Il secondo capitolo invece, sarà incentrato sulla fisica e su come il formalismo 3+1 agisce nella teoria della relatività generale.
L'argomento principale sarà la decomposizione dell'equazione di Einstein che verrà successivamente trattata come un sistema di equazioni differenziali alle derivate parziali.
Sarà introdotto ed utilizzato il concetto di geometrodinamica (introdotto da Wheeler nei primi anni sessanta) per giungere all'approccio hamiltoniano alla relatività generale.
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Bergstedt, Viktor. "Spacetime as a Hamiltonian Orbit and Geroch's Theorem on the Existence of Fermions." Thesis, Uppsala universitet, Institutionen för fysik och astronomi, 2020. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-432488.
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Over a century since its inception, general relativity continues to lie at the heart of some of the most researched topics in theoretical physics. It seems likely that the coveted solutions to problems like quantum gravity are to be found in an extension of general relativity, one which may only be visible in an alternate formulation of the theory. In this thesis we consider the possibility of casting general relativity in the form of an initial value problem where spacetime is seen as the evolution of space. This evolution is shown to be constrained and of Hamiltonian type. Not all spacetimes are physically acceptable. To be compatible with particle physics, one would like spacetime to accommodate fermions. Here we can take comfort in Geroch’s theorem, which implies that any spacetime that admits a Hamiltonian formulation automatically supports the existence of fermions. We review the elements that go into the proof of this theorem.Allmän relativitetsteori har i över hundra år legat i teoretiska fysikens framkant. Det är möjligt att lösningarna på öppna problem som kvantiseringen av gravitation går att finna i en utvidgning av allmän relativitetsteori – och kanske uppenbarar sig denna utvidgning bara ur en alternativ formulering av teorin. I den här uppsatsen formuleras allmän relativitetsteori och dess Einsteinekvationer som ett begynnelsevärdesproblem, genom vilket rumtiden kan betraktas som rummets historia. Vi visar att rummets rörelseekvationer är Hamiltons ekvationer med tvångsvillkor. Enligt partikelfysiken bör fermioner kunna finnas till i rumtiden. Härom kan vi åberopa Gerochs sats, enligt vilken rumtider som har en Hamiltonsk formulering också medger fermioner. Vi redogör för huvuddragen i beviset av Gerochs sats.
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Radermacher, Katharina Maria. "Strong Cosmic Censorship and Cosmic No-Hair in spacetimes with symmetries." Doctoral thesis, KTH, Matematik (Avd.), 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-220400.
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This thesis consists of three articles investigating the asymptotic behaviour of cosmological spacetimes with symmetries arising in Mathematical General Relativity. In Paper A and B, we consider spacetimes with Bianchi symmetry and where the matter model is that of a perfect fluid. We investigate the behaviour of such spacetimes close to the initial singularity ('Big Bang'). In Paper A, we prove that the Strong Cosmic Censorship conjecture holds in non-exceptional Bianchi class B spacetimes. Using expansion-normalised variables, we further show detailed asymptotic estimates. In Paper B, we prove similar estimates in the case of stiff fluids. In Paper C, we consider T2-symmetric spacetimes satisfying the Einstein equations for a non-linear scalar field. To given initial data, we show global existence and uniqueness of solutions to the corresponding differential equations for all future times. In the special case of a constant potential, a setting which is equivalent to a linear scalar field on a background with a positive cosmological constant, we investigate in detail the asymptotic behaviour towards the future. We prove that the Cosmic No-Hair conjecture holds for solutions satisfying an additional a priori estimate, an estimate which we show to hold in T3-Gowdy symmetry.Denna avhandling består av tre artiklar som undersöker det asymptotiska beteendet hos kosmologiska rumstider med symmetrier som uppstår i Matematisk Allmän Relativitetsteori. I Artikel A och B studerar vi rumstider med Bianchi symmetri och där materiemodellen är en ideal fluid. Vi undersöker beteendet av sådana rumstider nära ursprungssingulariteten ('Big Bang'). I Artikel A bevisar vi att den Starka Kosmiska Censur-förmodan håller för icke-exceptionella Bianchi klass B-rumstider. Med hjälp av expansions-normaliserade variabler visar vi detaljerade asymptotiska uppskattningar. I Artikel B visar vi liknande uppskattningar för stela fluider. I Artikel C betraktar vi T2-symmetriska rumstider som uppfyller Einsteins ekvationer för ett icke-linjärt skalärfält. För givna begynnelsedata visar vi global existens och entydighet av lösningar till motsvarande differentialekvationer för all framtid. I det speciella fallet med en konstant potential, en situation som motsvarar ett linjärt skalärfält på en bakgrund med en positiv kosmologisk konstant, undersöker vi i detalj det asymptotiska beteendet mot framtiden. Vi visar att den Kosmiska Inget-Hår-förmodan håller för lösningar som uppfyller en ytterligare a priori uppskattning, en uppskattning som vi visar gäller i T3-Gowdy-symmetri.
QC 20171220
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Alessandrini, Federico. "L'equazione d'onda non omogenea in elettromagnetismo e in relatività generale." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23887/.
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In questo lavoro di tesi proponiamo di analizzare il legame tra le equazioni dell'elettromagnetismo di Maxwell e le equazioni di campo di Einstein, verificando come in opportune condizioni le seconde presentano una forma analoga alle prime.
Verranno ricapitolate alcune nozioni chiave dell'elettromagnetismo e della Relatività Ristretta, fondamentali per giungere alla formulazione covariante delle equazioni di Maxwell. In particolare, si analizzeranno le relazione tra il campo elettrico e magnetico ed i potenziali vettore e scalare, necessari per costruire il tensore del campo elettromagnetico ed il quadripotenziale.
Partendo poi da una breve introduzione delle equazioni di campo di Einstein, vedremo come, lavorando in condizioni di campo gravitazionale debole, sia possibile ottenere una forma linearizzata di queste ultime e di come essa presenti una struttura analoga all'equazione delle onde, o di d'Alembert.
Infine, presenteremo una soluzione analitica per questo tipo di equazioni differenziali. Utilizzando come caso applicativo l'equazione di Maxwell in forma tensoriale, introdurremo brevemente il concetto funzione di Green e di come applicarlo al caso dell'equazione di d'Alembert. Ne ricaveremo una forma esplicita, osservando come la richiesta di validità del principio di causalità imporrà un vincolo sulla scelta della soluzione, e di come questa porti poi alla definizione del potenziale ritardato.
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Cosentino, Angelo. "Torsione nello spaziotempo e teoria di Einstein-Cartan." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/13743/.
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Lo scopo primario del lavoro è quello di conferire allo spazio fisico una nuova proprietà geometrica: la torsione. L’idea generale è quella di tentare di proseguire il lavoro di Albert Einstein della teoria della relatività generale ed estendere i suoi principi geometrici anche al mondo microscopico. Sfrutterò appieno la geometrizzazione della teoria della gravitazione e mostrerò come aggiungere a quest'ultima la presenza del tensore di torsione rappresenti solo una leggera modifica alla teoria. La torsione, inizialmente considerata una proprietà geometrica aggiuntiva dello spaziotempo, sarà caratterizzata fisicamente attraverso il legame con una proprietà quantomeccanica intrinseca della materia: lo spin.
Presenterò un capitolo introduttivo in cui verrà ripercorso il cammino che ha portato Einstein alla teoria della relatività generale in modo qualitativo poiché la mia attenzione riguarderà l'evoluzione della struttura geometrica dello spazio fisico.
Nel secondo capitolo proverò a motivare la necessità di proseguire ulteriormente quel cammino e studiare quindi la teoria di Einstein-Cartan. Segue poi un capitolo di strumenti matematici necessari per poter studiare nel profondo la nuova geometria dello spaziotempo e la teoria nascente nel capitolo 4, in cui sono formulate le equazioni di campo. Per la loro formulazione sarà seguito un approccio di tipo variazionale.
Tali equazioni saranno poi discusse nel capitolo successivo in cui si vuole immediatamente mostrare come la teoria di Einstein-Cartan rappresenti una piccola modifica della teoria di Einstein seppur con predizioni nuove e interessanti. Nello stesso capitolo verrà stimato e discusso il dominio di validità dei risultati ottenuti e verrano presentati dei riferimenti in cui vengono discusse altre importanti conseguenze della teoria.
Segue infine un capitolo conclusivo in cui si vuole ripercorrere quanto fatto e si vuole anche mostrare quanto ancora ci sia da fare.
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Göransdotter, Rebecka. "Ett genis trovärdighet : En retorisk analys av Albert Einsteins vetenskapliga ethos." Thesis, Uppsala universitet, Litteraturvetenskapliga institutionen, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-354326.
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Albert Einstein published the English translation of Relativity: The Special and General Theory in the midst of two big events in 1920: the confirmation of the two theories of relativity and spacetime in 1919 and the Nobel prize in physics in 1921. The new global celebrity wanted to make the theories intelligible and readable for an international English-speaking audience, an audience that also included antagonistic scientists and even anti-Semites. The aim of this thesis is to do a rhetorical analysis of Einstein’s character, his ethos, in Relativity, with a specific focus on creation of credibility in regard to his historical context: scientific ideals, values and norms as well as the political and cultural tendencies in Europe during the early 20th century. This was done firstly by identifying the implied auditor. Secondly, based on the material, I have identified three stereotypes or characters – the professional idealist, the mentor and the internationalist – which emphases different features and capacities that are crucial for the credibility of the text. Thirdly, by using these stereotypes and in regard to the specific historical context, I investigated how Einstein developed his primary ethos into a secondary ethos in the text. The rhetorical analysis of Einstein’s Relativity shows that his ethos stands in relation to the social and cultural perception of the virtuous epistemic scientist; to fight prejudices regarding being a Jewish-German theoretical physicist; and, noteworthy, a way to produce a well-needed international space – a crucial alternative to continue the positivistic knowledge production counter to the nationalistic project.
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Frye, Christopher. "Modification to Einstein's field equations imposed by string theory and consequences for the classical tests of general relativity." Honors in the Major Thesis, University of Central Florida, 2013. http://digital.library.ucf.edu/cdm/ref/collection/ETH/id/852.
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String theory imposes slight modifications to Einstein's equations of general relativity (GR). In (4), the authors claim that the gravitational field equations in empty space, which in GR are just R [subscript greek letters mu nu ] = 0, should hold one extra term which is first order in the string constant [alpha'] and proportional to the Riemann curvature tensor squared. They do admit, however, that this simple modification is just schematic. In (1) the authors use modified equations which are coupled to the dilation field. We show that equations given in (4) do not admit an isotropic solution; justification of these equations would require sacrificing isotropy. We thus investigate the consequences of the coupled equations from (1) and the black-hole solution they give there. We calculate the additional perihelion precession of Mercury, the added deflection of photons by the sun, and the extra gravitational redshift which should be present if these equations hold. We determine that additional effects due to string theory in each of these cases are quite minuscule.B.S.
Bachelors
Sciences
Physics
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Mistretta, Giovanni. "La precessione di Mercurio." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23599/.
Full textAbstract:
L’obiettivo di questa tesi è ricavare e confrontare l’orbita di Mercurio sia nell’ambito
della fisica newtoniana sia utilizzando la teoria della Relatività Generale. Il testo si
sviluppa in tre capitoli. La prima parte si concentrerà sul "Problema di Keplero" e sulle
equazioni del moto della fisica classica, mettendo in luce che non è presente alcun moto
di precessione se non si considerano le perturbazioni dovute alla presenza degli altri corpi
del sistema solare. La seconda parte si occuperà di derivare la metrica di Schwarzschild
(corrispondente all’espressione di un campo gravitazionale generato da una distribuzione
sferica di massa) e di utilizzare l’equazione di Hamilton-Jacobi relativistica per ottenere
l’orbita. Vedremo che, nell’ambito della Relatività Generale, il moto di precessione non
solo è previsto già per il sistema Sole-Mercurio ma è in estremo accordo con i dati
sperimentali. L’ultimo capitolo è dedicato alla descrizione dell’articolo di Einstein del
1915, in cui venne studiata e calcolata per la prima volta la precessione di Mercurio.
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Lachaume, Xavier. "Des équations de contrainte en gravité modifiée : des théories de Lovelock à un nouveau problème de σk-Yamabe." Thesis, Tours, 2017. http://www.theses.fr/2017TOUR4018/document.
Full textAbstract:
Cette thèse est consacrée au problème d’évolution des théories de gravité modifiée : après avoir rappelé ce qu’il en est pour la Relativité Générale (RG), nous exposons le formalisme n + 1 des théories ƒ(R), Brans-Dicke et tenseur-scalaire et redémontrons un résultat connu : le problème de Cauchy est bien posé pour ces théories, et les équations de contrainte se réduisent à celles de la RG avec un champ de matière. Puis nous effectuons la même décomposition n + 1 pour les théories de Lovelock et, ce qui est nouveau, ƒ(Lovelock). Nous étudions ensuite les équations de contrainte des théories de Lovelock et montrons qu’elles sont, dans le cas conformément plat et symétrique en temps, la prescription d’une somme de σk-courbures. Afin de résoudre cette équation de prescription, nous introduisons une nouvelle famille de polynômes semi-symétriques homogènes et développons des résultats de concavité pour ces polynômes. Nous énonçons une conjecture qui, si elle était avérée, nous permettrait de résoudre l’équation de prescription dans de nombreux cas : ∀ P;Q ∈ ℝ[X], avec deg P = deg Q = p, P et Q sont scindés => p ∑ k=0 P(k) Q(p-k) est scindéThis thesis is devoted to the evolution problem for modified gravity theories. After having explained this problem for General Relativity (GR), we present the n + 1 formalism for ƒ(R) theories, Brans-Dicke and scalar-tensor theories. We recall a known result: the Cauchy problem for these theories is well-posed, and the constraint equations are reduced to those of GR with a matter field. Then we proceed to the same n+1 decomposition for Lovelock and ƒ(Lovelock) theories, the latter being an original result. We show that in the locally conformally flat timesymmetric case, they can be written as the prescription of a sum of σk-curvatures. In order to solve the prescription equation, we introduce a new family of homogeneous semisymmetric polynomials and prove some concavity results for those polynomials. We express the following conjecture: if this is true, we are able to solve the prescription equation in many cases. ∀ P;Q ∈ ℝ[X], avec deg P = deg Q = p, P and Q are real-rooted => p ∑ k=0 P(k) Q(p-k) is real-rooted:
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Hadad, Yaron. "Integrable Nonlinear Relativistic Equations." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/293490.
Full textAbstract:
This work focuses on three nonlinear relativistic equations: the symmetric Chiral field equation, Einstein's field equation for metrics with two commuting Killing vectors and Einstein's field equation for diagonal metrics that depend on three variables. The symmetric Chiral field equation is studied using the Zakharov-Mikhailov transform, with which its infinitely many local conservation laws are derived and its solitons on diagonal backgrounds are studied. It is also proven that it is equivalent to a novel equation that poses a fascinating similarity to the Sinh-Gordon equation. For the 1+1 Einstein equation the Belinski-Zakharov transformation is explored. It is used to derive explicit formula for N gravitational solitons on arbitrary diagonal background. In particular, the method is used to derive gravitational solitons on the Einstein-Rosen background. The similarities and differences between the attributes of the solitons of the symmetric Chiral field equation and those of the 1+1 Einstein equation are emphasized, and their origin is pointed out. For the 1+2 Einstein equation, new equations describing diagonal metrics are derived and their compatibility is proven. Different gravitational waves are studied that naturally extend the class of Bondi-Pirani-Robinson waves. It is further shown that the Bondi-Pirani-Robinson waves are stable with respect to perturbations of the spacetime. Their stability is closely related to the stability of the Schwarzschild black hole and the relation between the two allows to conjecture about the stability of a wide range of gravitational phenomena. Lastly, a new set of equations that describe weak gravitational waves is derived. This new system of equations is closely and fundamentally connected with the nonlinear Schrödinger equation and can be properly called the nonlinear Schrödinger-Einstein equations. A few preliminary solutions are constructed.
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Piolanti, Simone. "Il formalismo ADM per la metrica FLRW." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2020.
Find full textAbstract:
Il tema centrale di questo elaborato è la cosmologia, affrontata in ambito di relatività generale applicando il formalismo ADM al modello FLRW. Il problema consiste nella risoluzione delle equazioni di Einstein in presenza di materia. Sfruttando quindi il formalismo ADM sono innanzitutto definite le formulazioni lagrangiana ed hamiltoniana di una teoria in ambito di relatività generale. In particolare sono descritte tali formulazioni per le equazioni di Einstein. Segue come applicazione l'esempio della particella libera relativistica interpretata come teoria di campo in una dimensione. È infine trattato il caso di interesse: si considera la metrica FLRW per universo piatto e sono risolte le equazioni di Einstein calcolate a partire da un'azione in cui la materia è descritta da un campo scalare senza massa di minimo accoppiamento.
Il risultato ottenuto descrive due possibili universi: uno in espansione e uno in contrazione. In particolare, l'evoluzione del fattore di scala rispetto al tempo proprio del sistema è descritto dalla relazione α^3 (τ)=α^3 (0)(1±τ/τ_c).
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Gustafsson, Emil. "Simple cosmological models and their descriptions of the universe." Thesis, Linköpings universitet, Matematik och tillämpad matematik, 2018. http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-153329.
Full textAbstract:
Cosmology is the study of the universe as a whole, and attempts to describe the behaviour of the universe mathematically. The simplest relativistic cosmological models are derived from Einstein's field equations with the assumptions of isotropy and homogeneity. In this thesis, a few simple cosmological models will be derived and evaluated with respect to their description of our universe i.e., how well they match observational data from e.g., the cosmic background radiation and redshift from distant supernovae. The models are derived from Einstein's field equations, which is why a large portion of the thesis will lay the ground work for the field equations by introducing and explaining the language of tensors.Kosmologi är läran om universum i stort samt dess matematiska beskrivning. De enklaste relativistiska kosmologiska modellerna kan härledas från Einsteins fältekvationer med hjälp av antaganden om isotropi och homogenitet. I denna rapport kommer ett par av de enklaste modellerna att härledas, samt evalueras baserat på hur väl de beskriver vårt universum, det vill säga hur bra de passar de observationer som gjorts på exempelvis den kosmiska bakgrundsstrålningen och rödskifte från avlägsna supernovor. Modellerna härleds utifrån Einsteins fältekvationer, varför en stor del av rapporten består av en introduktion till tensoranalys.
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Docherty, Peter. "Generalised Robinson-Trautman and Kundt waves and their physical interpretation." Thesis, Loughborough University, 2004. https://dspace.lboro.ac.uk/2134/13508.
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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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Casadei, Lorenzo. "Gravità teleparallela." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2014. http://amslaurea.unibo.it/6842/.
Full textAbstract:
Questo elaborato espone l'equivalenza tra la relatività generale di Einstein e una teoria poco conosciuta chiamata Gravità Teleparallela. Sebbene possono sembrare diverse, esse sono due modi equivalenti di vedere l'universo, la prima con spaziotempo curvo, curvatura e traiettorie geodetiche; la seconda con spazio piatto e la curvatura che si comporta come una forza. Per queste teorie si rivelano fondamentali elementi di geometria differenziale e tensoriale, come i tensori metrici, tensori di Riemann, derivate covarianti, oltre ai concetti fisici di tetrade, connessioni di Lorentz, sistemi inerziali e non.
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Calcinari, Andrea. "Effetti delle onde gravitazionali attraverso la deviazione geodetica." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2017. http://amslaurea.unibo.it/14076/.
Full textAbstract:
L'intento perseguito nel redigere questa tesi è quello di illustrare la teoria alla base delle onde gravitazionali per giungere ad intuire i metodi che ne consentono la rilevazione. Queste sono una conseguenza della Teoria della Relatività Generale di cui si riporta una semplice introduzione nel primo capitolo, sottolineando l'importanza del formalismo geometrico e tensoriale. Le equazioni di Einstein descrivono il campo gravitazionale come curvatura
dello spaziotempo, questa è rappresentata dal tensore di Riemann che determina
in particolare l'accelerazione relativa di due geodetiche. Si studia poi l'approssimazione di campo debole, necessaria per linearizzare le equazioni di Einstein
e per mostrare che la perturbazione metrica soddisfa
un'equazione d'onda. Il capitolo terzo si conclude quindi con un'analogia tra le onde gravitazionali
e quelle elettromagnetiche. Nel quarto capitolo si analizzano le
soluzioni sotto forma di onde piane: qui emergono caratteristiche peculiari riguardanti la perturbazione gravitazionale che, con il giusto gauge, permette di
dedurre che solo due sono le polarizzazioni fisicamente rilevanti e che sono trasversali rispetto
alla direzione dell'onda. Infine si evince che è necessario un sistema di
particelle per la rilevazione di un'onda perchè la grandezza da osservare è la separazione
tra due geodetiche e come questa varia al passaggio dell'onda. In questo modo viene mostrata
la causa degli effetti mareali e si confermano
le caratteristiche della radiazione gravitazionale anticipate in precedenza, come la
polarizzazione e la natura quadripolare. Alcune considerazioni matematiche finali elucideranno
come le proprietà delle onde suggeriscono con naturalezza l'esistenza di una radiazione
di gravità. Infine si accennerà alle idee chiave che hanno
suggerito la costruzione di rilevatori di onde e come questi debbano funzionare. La trattazione
termina con uno sguardo alle recenti scoperte e alle aspettative future.
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Sebastianutti, Marco. "Geodesic motion and Raychaudhuri equations." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2019. http://amslaurea.unibo.it/18755/.
Full textAbstract:
The work presented in this thesis is devoted to the study of geodesic motion in the context of General Relativity. The motion of a single test particle is governed by the geodesic equations of the given space-time, nevertheless one can be interested in the collective behavior of a family (congruence) of test particles, whose dynamics is controlled by the Raychaudhuri equations. In this thesis, both the aspects have been considered, with great interest in the latter issue. Geometric quantities appear in these evolution equations, therefore, it goes without saying that the features of a given space-time must necessarily arise. In this way, through the study of these quantities, one is able to analyze the given space-time. In the first part of this dissertation, we study the relation between geodesic motion and gravity. In fact, the geodesic equations are a useful tool for detecting a gravitational field. While, in the second part, after the derivation of Raychaudhuri equations, we focus on their applications to cosmology. Using these equations, as we mentioned above, one can show how geometric quantities linked to the given space-time, like expansion, shear and twist parameters govern the focusing or de-focusing of geodesic congruences. Physical requirements on matter stress-energy (i.e., positivity of energy density in any frame of reference), lead to the various energy conditions, which must hold, at least in a classical context. Therefore, under these suitable conditions, the focusing of a geodesics "bundle", in the FLRW metric, bring us to the idea of an initial (big bang) singularity in the model of a homogeneous isotropic universe. The geodesic focusing theorem derived from both, the Raychaudhuri equations and the energy conditions acts as an important tool in understanding the Hawking-Penrose singularity theorems.
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Krupanandan, Daniel D. "Solution generating algorithms in general relativity." Thesis, 2011. http://hdl.handle.net/10413/9766.
Full textAbstract:
We conduct a comprehensive investigative review of solution generating algorithms
for the Einstein field equations governing the gravitational behaviour of an isolated
neutral static spherical distribution of perfect fluid matter. Traditionally, the master
field equation generated from the condition of pressure isotropy has been interpreted
as a second order ordinary differential equation. However, since the pioneering work
of Wyman (1949) it was observed that more success can be enjoyed by regarding
the equation as a first order linear differential equation. There was a resurgence
of the ideas of Wyman in 2000 and various researchers have been able to generate
complete solutions to the field equations up to certain integrations. These have
been accomplished by working in Schwarzschild (curvature) coordinates, isotropic
coordinates, area coordinates and a coordinate system written in terms of the redshift
parameter. We have utilised Durgapal–Banerjee (1983) coordinates and produced a
new algorithm. The algorithm is used to generate new classes of perfect fluid solutions
as well as to regain familiar particular solutions reported in the literature. We find
that our solution is well behaved according to elementary physical requirements.
The pressure vanishes for a certain radius and this establishes the boundary of the
distribution. Additionally the pressure and energy density are both positive inside
the radius. The energy conditions are shown to be satisfied and it is particularly
pleasing to have the causality criterion satisfied to ensure that the speed of light is
not exceeded by the speed of sound. We also report some new solutions using the
algorithms proposed by Lake (2006).Thesis (M.Sc.)-University of KwaZulu-Natal, Westville, 2011.
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Thirukkanesh, Suntharalingam. "New analytical stellar models in general relativity." Thesis, 2009. http://hdl.handle.net/10413/435.
Full textAbstract:
We present new exact solutions to the Einstein and Einstein-Maxwell field equations that model the interior of neutral, charged and radiating stars. Several new classes of solutions in static spherically symmetric interior spacetimes are found in the presence of charge. These correspond to isotropic matter with a specified electric field intensity. Our solutions are found by choosing different rational forms for one of the gravitational potentials and a particular form for the electric field. The models generated contain results found previously including Finch and Skea (1989) neutron stars, Durgapal and Bannerji (1983) dense stars, Tikekar (1990) superdense stars in the limit of vanishing charge. Then we study the general situation of a compact relativistic object with anisotropic pressures in the presence of the electromagnetic field. We assume the equation of state is linear so that the model may be applied to strange stars with quark matter and dark energy stars. Several new classes of exact solutions are found, and we show that the densities and masses are consistent with real stars. We regain as special cases the Lobo (2006) dark energy stars, the Sharma and Maharaj (2007) strange stars and the realistic isothermal universes of Saslaw et al (1996). In addition, we consider relativistic radiating stars undergoing gravitational collapse when the fluid particles are in geodesic motion. We transform the governing equation into Bernoulli, Riccati and confluent hypergeometric equations. These admit an infinite family of solutions in terms of simple elementary functions and special functions. Particular models contain the Minkowski spacetime and the Friedmann dust spacetime as limiting cases. Finally, we model the radiating star with shear, acceleration and expansion in the presence of anisotropic pressures. We obtain several classes of new solutions in terms of arbitrary functions in temporal and radial coordinates by rewriting the junction condition in the form of a Riccati equation. A brief physical analysis indicates that these models are physically reasonable.Thesis (Ph.D.)-University of KwaZulu-Natal, Westville, 2009.
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Moodley, Jothi. "Applications of embedding theory in higher dimensional general relativity." Thesis, 2012. http://hdl.handle.net/10413/10594.
Full textAbstract:
The study of embeddings is applicable and signicant to higher dimensional theories of
our universe, high-energy physics and classical general relativity. In this thesis we investigate
local and global isometric embeddings of four-dimensional spherically symmetric
spacetimes into five-dimensional Einstein manifolds. Theorems have been established
that guarantee the existence of such embeddings. However, most known explicit results
concern embedded spaces with relatively simple Ricci curvature. We consider the four-dimensional
gravitational field of a global monopole, a simple non-vacuum space with
a more complicated Ricci tensor, which is of theoretical interest in its own right, and
occurs as a limit in Einstein-Gauss-Bonnet Kaluza-Klein black holes, and we obtain
an exact solution for its embedding into Minkowski space. Our local embedding space
can be used to construct global embedding spaces, including a globally
at space and
several types of cosmic strings. We present an analysis of the result and comment on
its signicance in the context of induced matter theory and the Einstein-Gauss-Bonnet
gravity scenario where it can be viewed as a local embedding into a Kaluza-Klein black
hole. Difficulties in solving the five-dimensional equations for given four-dimensional
spaces motivate us to investigate which embedded spaces admit bulks of a specific type.
We show that the general Schwarzschild-de Sitter spacetime and the Einstein Universe
are the only spherically symmetric spacetimes that can be embedded into an Einstein
space with a particular metric form, and we discuss their five-dimensional solutions.
Furthermore, we determine that the only spherically symmetric spacetime in retarded
time coordinates that can be embedded into a particular Einstein bulk is the general
Vaidya-de Sitter solution with constant mass. These analyses help to provide insight to
the general embedding problem. We also consider the conformal Killing geometry of a
five-dimensional Einstein space that embeds a static spherically symmetric spacetime,
and we show how the Killing geometry of the embedded space is inherited by its bulk.
The study of embedding properties such as these enables a deeper mathematical understanding
of higher dimensional cosmological models and is also of physical interest
as conformal symmetries encode conservation laws.Thesis (Ph.D.)-University of KwaZulu-Natal, Durban, 2012.
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Spillane, Matthew. "The Einstein equations in the null quasi-spherical gauge." Phd thesis, 1994. http://hdl.handle.net/1885/138374.
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Anderson, Matthew William Matzner Richard A. "Constrained evolution in numerical relativity." 2004. http://wwwlib.umi.com/cr/utexas/fullcit?p3139182.
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Anderson, Matthew William. "Constrained evolution in numerical relativity." Thesis, 2004. http://hdl.handle.net/2152/1182.
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