Dissertations / Theses on the topic 'General Relativity'
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Galal, Mohamed. "Etude dans les espaces-temps de dimension arbitraire : Tenseurs de Bel et Robinson. Equations de spin élevé." Paris 6, 1986. http://www.theses.fr/1986PA066674.
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Depuis 1921, date a laquelle kaluza elabora une theorie unitaire pentadimensionnelle, qui realisait une unification des champs gravitionnel et electromagnerique; les essais de construire une theorie unitaire, au sein d'une structure geometrique pour l'univers de dimension superieure a quatre, se sont multiplies. Cette voie a ete confirmee par l'apparition de la theorie de supergravite. Des lors, il fallait regarder tous les parametres de la relativite generale classique dans des varietes pseudoriemanniennes de dimension arbitraire. Ce travail s'inscrit dans cette demarche. Nous avons generalise les tenseurs de bel et robinson en dimension arbitraire. Nous avons precise que ces tenseurs sont distincts, ils coincident, si, et seulement si, l'espace est d'einstein de dimension quatre. Nous avons trouve que ces deux tenseurs sont conservatifs quelle que soit la dimension de l'espace. Cela represente la premiere partie du travail. Dans la deuxieme partie, nous avons trouve les conditions d'integrabilite d'un systeme de deux equations de type de dirac, pour un spin eleve en utilisant l'isomorphisme entre l'algebre exterieur et l'algebre de clifford
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Steele, John D. "Symmetries in general relativity." Thesis, University of Aberdeen, 1989. http://digitool.abdn.ac.uk/R?func=search-advanced-go&find_code1=WSN&request1=AAIU498554.
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The purpose of this thesis is to study those non-flat space-times in General Relativity admitting high dimensional Lie groups of motions, homotheties, conformals and affines, and to prove a theorem on the relationship between the first three of these. The basic theories and notations of differential geometry are set up first, and a useful theorem on first-order partial differential equations is proved. The concepts of General Relativity are introduced, space-times are defined and a brief account of the well-known Petrov and Segre classifications is given. The interplay between these classifications and the isotropy structure of the various Lie groups is discussed as is the so-called 'Schmidt method'. Generalised p.p. waves are studied, with a special study of the subclass of generalised plane waves undertaken, many different characterisations of these latter are found and their admitted symmetries are completely described. Motions, homotheties and affines are considered. A survey of symmetries in Minkowski space, and a summary of known results on space-times with high dimensional groups of motions is given. The problem of r-dimensional groups of homotheties is studied. The r 6 cases are completely resolved, and examples in the r = 5 cases are given. All examples of non-flat space-times admitting the maximal group of affines are displayed, correcting an error in the literature. The thesis ends with a proof of the Bilyalov-Defrise-Carter theorem, which states that for any non conformally flat space-time there is a conformally related metric for which the original group of conformals is a group of homotheties (motions if not conformal to generalised plane waves). The proof given does not use Bilyalov's analyticity assumption, and is more geometric than Defrise-Carter. The maximum size of the conformal group for a given Petrov type is found. An appendix gives a brief account of some REDUCE routines used to check some algebraic manipulations.
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Bondarescu, Mihai Barish Barry C. Barish Barry C. "Topics in general relativity /." Diss., Pasadena, Calif. : California Institute of Technology, 2007. http://resolver.caltech.edu/CaltechETD:etd-05282007-231321.
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Samuelsson, Lars. "Stellar Models in General Relativity." Doctoral thesis, Stockholm : Univ, 2003. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-13.
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Eriksson, Daniel. "Perturbative Methods in General Relativity." Doctoral thesis, Umeå : Department of Physics, Umeå University, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-1488.
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Swing, André. "Experimental Tests of General Relativity." Thesis, KTH, Teoretisk fysik, 2013. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-127006.
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Abstract This paper treats Einstein's theory of General Relativity (GR), in particular three of the earliest experiments testing its validity. It covers the de ection of, and the redshift of light in a gravity eld, two new phenomena predicted by GR. The perihelion precession of the planet Mercury and how GR matches observations of it more correctly than classic physics is also covered. In addition to the three older tests above, the more modern application in the GPS system is discussed, and how it can be regarded as a test of GR. Some theoretical questions are also discussed, including comparing classic physics to GR and the classical limit of GR.Denna rapport handlar om Einsteins allmäna relativitetstori (GR), och mer specikt om tre tidiga experiment som kan testa dess giltlighet. Här behandlas avböjning av, och rödförskjutning av ljus i gravitationsfält, två nya fenomen som förutsägs av GR. Planeten merkurius periheliumprecession och hur GR bättre matchar observationer av den täcks också upp. Förutom dessa tre experiment, diskuteras också tillämpningen av GR i GPS-systemet, och hur det kan betraktas som ett test av GR. Några teoretiska frågor diskuteras också; bland annat jämförs klassisk fysik med GR och den klassiska gränsen till GR tas upp.
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Low, David J. "Affine symmetry in general relativity." Thesis, University of Aberdeen, 1994. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.386299.
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Affine vector fields in 4-dimensional Lorentz manifolds have recently been investigated in some detail by Hall and da Costa. The picture is completed in this thesis by studying the zeros of affine vector fields. Hall and da Costa show that the problem of finding affine vector fields in non-degenerately reducible 4-dimensional Lorentz manifolds can be reduced, with one exceptional case, to the problem of finding homothetic vector fields in lower dimensional manifolds. This means that the study of affine vector fields with zeros in 4-dimensional Lorentz manifolds is aided by investigating proper homothetic and Killing vector fields with zeros in 2- or 3-dimensional manifolds. To this end proper homothetic vector fields with zeros are investigated in 2- and 3-dimensional Manifolds using techniques similar to those used by Hall. It is shown that in the 2-dimensional case the zero is necessarily isolated, whereas in the 3-dimensional case the zero set may either be isolated or 1-dimensional. In the latter case the manifold is shown to be a 3-dimensional plane wave space-time, and all of the affine and conformal vector fields that it admits are found. These results are then used to determine the nature of the zero sets of affine vector fields in 4-dimensional Lorentz manifolds. The algebraic structure of the Riemann, Ricci and Weyl tensors at such zeros is also described. This work is extended by studying affine vector fields, and their zero sets, in 3-dimensional Lorentz manifolds. An investigation of the zero sets of affine vector fields in 3- and 4-dimensional positive-definite manifolds is included for comparison.
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Kini, Dominic Anant. "Weak singularities in general relativity." Thesis, University of Southampton, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.241863.
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Iberê, Oliveira Kuntz de Souza. "Gravitational theories beyond general relativity." Thesis, University of Sussex, 2018. http://sro.sussex.ac.uk/id/eprint/80678/.
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Despite the success of general relativity in explaining classical gravitational phenomena, several problems at the interface between gravitation and high energy physics remain open to date. The purpose of this thesis is to explore classical and quantum gravity in order to improve our understanding of different aspects of gravity, such as dark matter, gravitational waves and ination. We focus on the class of higher derivative gravity theories as they naturally arise after the quantization of general relativity in the framework of effective field theory. The inclusion of higher order curvature invariants to the action always come in the form of new degrees of freedom. From this perspective, we introduce a new formalism to classify gravitational theories based on their degrees of freedom and, in light of this classification, we argue that dark matter is no different from modified gravity. Additional degrees of freedom appearing in the quantum gravitational action also affect the behaviour of gravitational waves. We show that gravitational waves are damped due to quantum degrees of freedom and we investigate the backreaction of these modes. The implications for gravitational wave events, such as the ones recently observed by the Advanced LIGO collaboration, are also discussed. The early universe can also be studied in this framework. We show how ination can be accommodated in this formalism via the generation of the Ricci scalar squared, which is triggered by quantum effects due to the non-minimal coupling of the Higgs boson to gravity, avoiding instability issues associated with Higgs ination. We argue that the non-minimal coupling of the Higgs to the curvature could also solve the vacuum instability issue by producing a large effective mass for the Higgs, which quickly drives the Higgs field back to the electroweak vacuum during ination.
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Baker, Theresa Mary. "Cosmological tests of general relativity." Thesis, University of Oxford, 2013. http://ora.ox.ac.uk/objects/uuid:dd5fda2f-d552-4130-839c-71c1a375ef49.
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Understanding the apparent accelerating expansion rate of the universe is a challenge for modern cosmology. One category of explanations is that we are using the wrong gravitational physics to study the observations. Our paradigmatic theory of gravity – Einstein’s theory of General Relativity – may be subsumed by a larger theory. This thesis develops a selection of tools for testing General Relativity and the numerous alternative theories of gravity that have been put forward. I advocate that an elegant and efficient way to test this space of theories is through the use of parameterized frameworks. Inspired by the Parameterized Post-Newtonian framework I develop a new formalism, the Parameterized Post-Friedmann formalism, that aims to unify the linear cosmological perturbation theory of many alternatives to General Relativity. Having introduced the Parameterized Post-Friedmann formalism and demonstrated its application via a suite of examples, I examine several issues surrounding parameterized tests of gravity. I first consider how the structure of a parameterization can influence the constraints obtainable from a given set of data. I then consider how to describe the growth of the large-scale structure of the universe in a parameterized manner. This leads to a convenient tool for calculating corrections to the growth rate of structure in modified theories, which can be used both with the Parameterized Post-Friedmann formalism or independently of it. I present forecasts for how well generalized deviations from General Relativity will be constrained by the next generation of galaxy surveys. Throughout, this thesis aims to take a synoptic approach to theories of modified gravity, rather than focussing on specific models. A question yet to be answered is whether this approach is realistic in practical terms. The final part of this thesis takes the first steps towards an answer.
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Sjödin, Robert. "Cosmic strings in general relativity." Thesis, University of Southampton, 2001. https://eprints.soton.ac.uk/50619/.
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In this thesis we examine the properties of Cosmic Strings in the theory of General Relativity. We begin by considering static Cosmic Strings in flat space-time. We derive the field equations for the Cosmic String and show that the solution depends upon a single scaling parameter a which is constructed from the physical constants. Using this result we construct 1-parameter families of solutions which depend on an auxiliary parameter e and which describe the thin-string limit of a Cosmic String. By interpreting these solutions as elements of the simplified Colombeau algebra we may interpret the relativistic energy density Too of the thin string as an element of the Colombeau algebra with delta-function mass-per-unit-length. Furthermore, for a critically coupled Cosmic String the energymomentum tensor in the thin-string limit may be given a distributional interpretation. We also solve the string equations numerically for various values of a. This is done by compactifying the space-time to include infinity as part of the numerical grid and then using a relaxation method to suppress exponentially growing un-physical solutions. In curved space-time we derive the equations for the scalar and vector fields which are now coupled to the geometric variables through Einstein's equations. We again examine the thin-string limit in the Colombeau algebra by considering a 1-parameter family of solutions. W'e derive an expression for the deficit angle in terms of the distributional energy-momentum tensor of the thin string. We use this result to investigate the gravitational lensing properties of the string and relate this to the deficit angle. In the special case of a cone we find the scattering angle is equal to the deficit angle. We also solve the coupled equations numerically using techniques similar to those used in flat space-time. The second part of the thesis involves the dynamics of Cosmic Strings. Einstein's equations then lead to wave equations for both the matter and metric variables. However, the space-time is not asymptotically flat and this leads to problems in applying the appropriate boundary conditions. By using a Geroch transformation it is possible to reformulate the equations in terms of geometrical variables defined on an asymptotically flat (2+l)-dimensional space-time. Three exact vacuum solutions describing gravitational radiation due to Weber-Wheeler, Xanthopoulos and Piran et al. are used to excite the string which is found to oscillate with frequencies which are proportional to the masses of the scalar and vector fields of the string. This is in agreement with the exact results obtained using the linearised equations of the thin dynamic string. The behaviour of the dynamic string is studied by solving the equations numerically using an implicit fully characteristic scheme. The use of the Geroch transformation allows us to compactify the space-time and include null infinity as part of the numerical grid. This enables us to use the correct boundary conditions at infinity and hence suppress un-physical divergent solutions. The code is tested by comparing the results with exact solutions, by checking that it agrees with the static code and by undertaking a time dependent convergence test. The code is found to be accurate, stable and exhibit clear second order convergence.
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Abdelfattah, Derhham. "General Relativity and penrose process." Master's thesis, University of Cape Town, 2016. http://hdl.handle.net/11427/28961.
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Taliotis, Anastasios S. "Evolving Geometries in General Relativity." The Ohio State University, 2010. http://rave.ohiolink.edu/etdc/view?acc_num=osu1274838401.
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Fransson, Kajsa. "General Relativity and Dynamical Universes." Thesis, Uppsala universitet, Teoretisk fysik, 2021. http://urn.kb.se/resolve?urn=urn:nbn:se:uu:diva-448902.
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The aim of this report is to explore different models of cosmology, depending on components as matter, radiation and dark energy. To be able to investigate the behaviour and age of these model universes, it is necessary to solve the Friedmann equation. Therefore a substantial part of this thesis is a study of general relativity, including mathematical tools as Riemannian geometry and the concept of curved space-time.Denna rapport ämnar att utforska olika kosmologiska modeller beroende på innehåll som materia, strålning och mörk energi. För att undersöka beteendet och åldern av dessa modellerade universa så är det nödvändigt att lösa Friedmann-ekvationen. Därför ägnas en betydande del av detta arbete åt att studera allmän relativitetsteori, med matematiska verktyg som Riemanngeometri och konceptet krökt rum-tid.
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Bello, Arufe Aaron. "Gravitational Waves in General Relativity." Thesis, Umeå universitet, Institutionen för fysik, 2017. http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-136721.
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In this paper, we write a summary about general relativity and, in particular,gravitational waves. We start by discussing the mathematics that generalrelativity uses, as well as the geometry in general relativity's spacetime. Afterwards,we explain linearized general relativity and derive the linearizedversions of Einstein's equations. From here, we construct wave solutionsand explain the polarization of gravitational waves. The quadrupole formulais derived, and generation and detection of gravitational waves is brie ydiscussed. Finally, LIGO and its latest discovery of gravitational waves isreviewed.
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O'Donnell, N. "Electromagnetic radiation reaction in general relativity." Thesis, Bucks New University, 1988. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.384632.
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Adam, Alexander. "Numerical general relativity in exotic settings." Thesis, Imperial College London, 2013. http://hdl.handle.net/10044/1/24825.
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In this thesis, we discuss applications of numerical relativity in a variety of complex settings. After introducing aspects of black hole physics, extra dimensions, holography, and Einstein-Aether theory we discuss how one can frame the problem of solving the static Einstein equations as an elliptic boundary value problem by inclusion of a DeTurck gauge fixing term. Having setup this background, we turn to our simplest application of numerical relativity, namely fractionalisation in holographic condensed matter. We explain how one may describe this phenomenon by studying particular classes of hairy black holes and analysing whether bulk flux is sourced by a horizon or charged matter. This problem is our simplest application of numerical relativity as the Einstein equations reduce to ODEs and the problem may be solved by shooting methods. We next turn to a discussion of stationary numerical relativity and explain how one can also view the problem of finding stationary black hole solutions as an elliptic problem, generalising the static results discussed earlier. Ergoregions and horizons are naively a threat to ellipticity, but by considering a class of spacetimes describing a fibration of the stationary and axial Killing directions over a Riemannian base space manifold, we show how the problem can nevertheless still be phrased in this manner. Finally we close with a discussion of black holes in Einstein-Aether theory. These unusual objects have multiple horizons as a consequence of broken Lorentz symmetry, and in order to construct such solutions we explain how to generalise the PDE methods of previous sections to construct solutions interior to a metric horizon where the Harmonic Einstein equations cease to be elliptic. Using this new machinery we rediscover the spherically symmetric static black holes that have been found in the literature and moreover present the first known rotating solutions of the theory.
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Lanza, Antonio. "Application of multigrid to general relativity." Doctoral thesis, SISSA, 1986. http://hdl.handle.net/20.500.11767/4516.
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Numerical solutions CNakamura, 1981 and reference therein,
Piran and Stark, 1984) of Einsteinrs equations following the
collapse of axially symmetric rotating bodies show, for some value
of the initial ratio a/m, the formation of structure with a
toroidal shape around centrally condensed core. If by some
mechanisms, the aim ratio of the core is reduced Csee Miller and
De Felice, 1985 and De Felice et al., 1985 for a discussion of
such mechanisms) to a value less than unity then a rotating black
hole may be formed, which will be surrounded by a massive toroidal
structure.
Other situations in which toroidal structures may be relevant
are in the modelling of quasars, active galactic nuclei and other
similar objects which most probably contain black holes and thick
accretion disks.
So far the general relativistic description of these
situations had been restricted to the case in which the
self-gravity of the disk was negligible CAbramowicz et al., 1978
and Kozlowski et al. 1978) or to the case when both the
self-gravity of the disk and the rotation of the black hole could
be considered as perturbations CUill, 1974, 19751 to the
Schwarzschild black hole. However there may be situations in which
the mass of the disk or tori is comparable with that of a rotating
hole CUiita, 1985). In this case the full Einstein equations
should be solved for the perturbations induced by the self-gravity
of the matter to the Kerr black hole.
Moreover it is not clear yet whether the self gravity of the
disk induces runaway instability. Abramowicz et al. C1980), using
a very simple model of the black hole accretion disk system
suggested that this kind of instability could act in a few
dynamical time scales so that the disk itself could eventually be
eaten by the black hole. This instability occurs because the
growing black hole changes its gravitational field and therefore
the location of the cusp through which matter is accreted changes.
On the other hand, Uilson C1984), using models of non-self-gravitating disks in the Kerr metric, concluded that
there is no such kind of instability. A final answer to this
problem can be given only after sequences of equilibrium
configurations of self-gravitating disks or tori around black
holes for different masses ratio have been constructed. This means
solving numerically Einstein equations consistently with the given
distribution of matter.
Since the problem is quite complicated in structure and a
standard numerical method will not easily cope with it, we have
decided to use the Multigrid method CBrandt, 1977) which although
is complicated to program will deal naturally with the
difficulties of the model. As one of the first applications of the
method in general relativity Csee Choptuik and Unruh, 1986, for a
different one), we decided to solve few representative test
problems before solving the entire one.
The plan of the thesis is as follows. In Chapter I we review
the general theory of figure of equilibrium in Newtonian and
relativistic theories. Chapter II contains a discussion of
stationary and axisymmetric space-times and a derivation of
Einstein 1 s equations with the relative boundary conditions. Also,
included is a discussion and deriv~tion of the equations governing
the fluid configuration. Chapter III reviews some numerical
techniques used to solve Einstein's equations for stationary and
axisymmetric configurations, with particular emphasis to the
Multigrid which is the method applied by us. Chapter IV contains
an application of Hultigrid in general relativity in the case of
vacuum stationary and axisymmetric space-times. In Chapter V we
write down the equations for an infinitesimally thin disk around a
black hole in Newtonian and relativistic theories. Also, an
outline on how to apply the Multigrid in this case, is given.
Finally, Chapter VI contains the outline of the application to the
case of a self-gravitating toroidal structure around a rapidly
rotating black hole.
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Alberti, Giuseppe. "Statistical mechanics of self-gravitating systems in general relativity." Thesis, Toulouse 3, 2017. http://www.theses.fr/2017TOU30309/document.
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La mécanique statistique des systèmes auto-gravitants constitue un des plus fascinants et mystérieux champs de recherche. À cause de la nature à longue-portée de la force gravitationnelle, la notion usuelle d'équilibre statistique est modifiée, faisant de cette étude un problème hors-équilibre. Par conséquent, ces systèmes exhibent certaines propriétés particulières comme, par exemple, l'existence de transitions de phase associées à un effondrement gravitationnel. Le travail présenté dans cette thèse a comme but une description détaillée des transitions de phase dans un cadre général relativiste en considérant, en particulier, le cas des fermions auto-gravitants. La thèse est conceptuellement divisée en trois parties, selon le niveau de dégénérescence du système. D'abord, nous focalisons notre attention sur le cas des fermions dégénérés (T = 0), en étudiant en détail l'équilibre gravitationnel. Ensuite, en considérant la limite de haute température (T >> 1), nous montrons l'existence de deux types d'effondrement gravitationnel dans les séries d'équilibre. Enfin, nous explorons le cas général, en illustrant la présence des transitions de phase gravitationnelles, soit dans l'ensemble micro-canonique soit dans l'ensemble canoniqueThe statistical mechanics of self-gravitating systems constitutes one of the most fascinating and puzzling fields of research. Due to the long-range nature of the gravitational force, the usual notion of statistical equilibrium is modified, making of this study an out-of-equilibrium problem. As a consequence, these systems exhibit some peculiar features such as the occurrence of phase transitions associated with a gravitational collapse. The work presented in this thesis aims at providing a detailed description of the phase transitions in a general relativistic framework by considering, in particular, the case of self-gravitating fermions. The thesis is conceptually divided in three parts, according to the degeneracy level of the system. We firstly focus our attention on the case of degenerate fermions (T = 0), by studying in detail the gravitational equilibrium. Successively, considering the high temperature limit (T >> 1), we show the existence of two kinds of gravitational collapse in the series of equilibria. Finally, we explore the general case, by illustrating the occurrence of the gravitational phase transitions, in both microcanonical and canonical ensembles
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Ilhan, Ibrahim B. "Dynamics Of Extended Objects In General Relativity." Master's thesis, METU, 2009. http://etd.lib.metu.edu.tr/upload/12610981/index.pdf.
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In this thesis, multipole expansions of mass, momentum and stress density will be made for
a body in Newtonian mechanics. Using these definitionsmomentum, angular momentum, center of mass, force and torque are defined for N gravitationally interacting isolated bodies. Equations of motions of such a system are derived. Definitions of momentum, angular momentum, center of mass, force and torque are made in a relativistic theory. Dynamical (gravitational) skeleton is defined and the multipole moments of the dynamical skeleton are found. Equations of motion for a test body moving in a gravitational field are derived in terms of the multipole moments. Save the details of the derivations, no originality in this thesis is claimed: it is intended as a review of the subject.
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Khan, Muhsan A. "Holonomy and projective symmetry in general relativity." Thesis, University of Aberdeen, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.369628.
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A study of the holonomy group of space-time is undertaken and related to the Segre and Petrov types of then Weyl and E-tensors respectively. Attention is then focused on the E-tensor, and a theorem is proved which states that any space-time M can be disjointly decomposed into open sets on which the Segre type of the E-tensor is constant, the union of which if dense in M. This theorem is then applied to prove a similar theorem for the Ricci tensor using the principal null directions of the E-tensor. Finally, a study of proper projective symmetry in null and non-null Einstein-Maxwell and static, spherically symmetric space-times is performed. A theorem is proved which states that no proper projective symmetry is possible in any null Einstein-Maxwell space-times. This result is then extended to the non-null case under some general restrictions. The static, spherically symmetric space-times are then considered, and those admitting proper projective symmetry are completely determined. The proper projective vector fields are also explicitly calculated.
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Patel, Mohammed T. "Affine and projective symmetry in general relativity." Thesis, University of Aberdeen, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.401196.
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A result regarding the decomposition of space-time using the Reimann tensor is proved and applied to other decompositions, as well as to the study of projective symmetry. Affine and homothetic symmetries, including the zeros of proper homothetic vector fields and the orbit structure of affine, homothetic and Killing symmetries are also studied, and a link to plane wave space-times established. Projective symmetry is investigated in conformally flat perfect fluid space-times, whilst the non-existence of proper projective symmetry in certain space-times is proved. The form of the Killing vector fields in a constant curvature manifold of arbitrary dimension and arbitrary metric signature is derived.
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Sperhake, Ulrich. "Non-linear numerical schemes in general relativity." Thesis, University of Southampton, 2001. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.394106.
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Burd, A. B. "General relativity, scalar fields and cosmic strings." Thesis, University of Sussex, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.381635.
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Lemos, Jose Pizarro de Sande. "Shells, discs and homology in general relativity." Thesis, University of Cambridge, 1987. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.254240.
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Kunesch, Markus. "Numerical simulations of instabilities in general relativity." Thesis, University of Cambridge, 2018. https://www.repository.cam.ac.uk/handle/1810/283135.
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General relativity, one of the pillars of our understanding of the universe, has been a remarkably successful theory. It has stood the test of time for more than 100 years and has passed all experimental tests so far. Most recently, the LIGO collaboration made the first-ever direct detection of gravitational waves, confirming a long-standing prediction of general relativity. Despite this, several fundamental mathematical questions remain unanswered, many of which relate to the global existence and the stability of solutions to Einstein's equations. This thesis presents our efforts to use numerical relativity to investigate some of these questions. We present a complete picture of the end points of black ring instabilities in five dimensions. Fat rings collapse to Myers-Perry black holes. For intermediate rings, we discover a previously unknown instability that stretches the ring without changing its thickness and causes it to collapse to a Myers-Perry black hole. Most importantly, however, we find that for very thin rings, the Gregory-Laflamme instability dominates and causes the ring to break. This provides the first concrete evidence that in higher dimensions, the weak cosmic censorship conjecture may be violated even in asymptotically flat spacetimes. For Myers-Perry black holes, we investigate instabilities in five and six dimensions. In six dimensions, we demonstrate that both axisymmetric and non-axisymmetric instabilities can cause the black hole to pinch off, and we study the approach to the naked singularity in detail. Another question that has attracted intense interest recently is the instability of anti-de Sitter space. In this thesis, we explore how breaking spherical symmetry in gravitational collapse in anti-de Sitter space affects black hole formation. These findings were made possible by our new open source general relativity code, GRChombo, whose adaptive mesh capabilities allow accurate simulations of phenomena in which new length scales are produced dynamically. In this thesis, we describe GRChombo in detail, and analyse its performance on the latest supercomputers. Furthermore, we outline numerical advances that were necessary for simulating higher dimensional black holes stably and efficiently.
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Sandin, Patrik. "Cosmological Models and Singularities in General Relativity." Doctoral thesis, Karlstads universitet, Avdelningen för fysik och elektroteknik, 2011. http://urn.kb.se/resolve?urn=urn:nbn:se:kau:diva-8206.
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This is a thesis on general relativity. It analyzes dynamical properties of Einstein's field equations in cosmology and in the vicinity of spacetime singularities in a number of different situations. Different techniques are used depending on the particular problem under study; dynamical systems methods are applied to cosmological models with spatial homogeneity; Hamiltonian methods are used in connection with dynamical systems to find global monotone quantities determining the asymptotic states; Fuchsian methods are used to quantify the structure of singularities in spacetimes without symmetries. All these separate methods of analysis provide insights about different facets of the structure of the equations, while at the same time they show the relationships between those facets when the different methods are used to analyze overlapping areas. The thesis consists of two parts. Part I reviews the areas of mathematics and cosmology necessary to understand the material in part II, which consists of five papers. The first two of those papers uses dynamical systems methods to analyze the simplest possible homogeneous model with two tilted perfect fluids with a linear equation of state. The third paper investigates the past asymptotic dynamics of barotropic multi-fluid models that approach a `silent and local' space-like singularity to the past. The fourth paper uses Hamiltonian methods to derive new monotone functions for the tilted Bianchi type II model that can be used to completely characterize the future asymptotic states globally. The last paper proves that there exists a full set of solutions to Einstein's field equations coupled to an ultra-stiff perfect fluid that has an initial singularity that is very much like the singularity in Friedman models in a precisely defined way.Status of the paper "Perfect Fluids and Generic Spacelike Singularities" has changed from manuscript to published since the thesis defense.
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Durkee, Mark N. "New approaches to higher-dimensional general relativity." Thesis, University of Cambridge, 2011. https://www.repository.cam.ac.uk/handle/1810/240580.
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This thesis considers various aspects of general relativity in more than four spacetime dimensions. Firstly, I review the generalization to higher dimensions of the algebraic classification of the Weyl tensor and the Newman-Penrose formalism. In four dimensions, these techniques have proved useful for studying many aspects of general relativity, and it is hoped that their higher dimensional generalizations will prove equally useful in the future. Unfortunately, many calculations using the Newman-Penrose formalism can be unnecessarily complicated. To address this, I describe new work introducing a higher-dimensional generalization of the so-called Geroch-Held-Penrose formalism, which allows for a partially covariant reformulation of general relativity. This approach provides great simplifications for many calculations involving spacetimes which admit one or two preferred null directions. The next chapter describes the proof of an important result regarding algebraic classification in higher dimensions. The classification is based upon the existence of a particular null direction that is aligned with the Weyl tensor of the geometry in some appropriate sense. In four dimensions, it is known that a null vector field is such a multiple Weyl aligned null direction (WAND) if and only if it is tangent to a shearfree null geodesic congruence. This is not the case in higher dimensions. However, I have formulated and proved a partial generalization of the result to arbitrary dimension, namely that a spacetime admits a multiple WAND if and only if it admits a geodesic multiple WAND.Moving onto more physical applications, I describe how the formalism that we have developed can be applied to study certain aspects of the stability of extremal black holes in arbitrary dimension. The final chapter of the thesis has a rather different flavour. I give a detailed analysis of the properties of a particular solution to the Einstein equations in five dimensions: the Pomeransky-Sen'kov doubly spinning black ring. I study geodesic motion around this black ring and demonstrate the separability of the Hamilton-Jacobi equation for null, zero energy geodesics. I show that this unexpected separability can be understood in terms of a symmetry described by a conformal Killing tensor on a four dimensional spacetime obtained by a Kaluza-Klein reduction of the original black ring spacetime.
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Sarkar, Souvik. "Consequences of Quantum Mechanics in General Relativity." University of Cincinnati / OhioLINK, 2018. http://rave.ohiolink.edu/etdc/view?acc_num=ucin1535709090287102.
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Panassiti, Antonio. "General relativity limit of Brans-Dicke gravity." Master's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23344/.
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In Brans-Dicke gravity a scalar field non-minimally coupled with the curvature acts as a new gravitational degree of freedom in addition to the usual metric field of General Relativity. Usually, when the coupling ω of the scalar field diverges, the latter approaches a constant and the solutions of the theory reduce to those generated by the Einstein equations with the same energy-momentum tensor as source. However, in the limit ω → ∞, the static and spherically symmetric vacuum solutions, called Brans solutions, do not reduce to the Schwarzschild metric, the only solution of General Relativity with the same type of symmetry. In this work we test their limit with a new method. Unlike the usual way, we use the Brans solutions to take the limit at the level of the equations. Since these are non-linear field equations depending on ω, in principle our procedure could lead to a different outcome. In particular, we take advantage of the Einstein frame formulation of the Brans-Dicke theory and we check if the solutions are able to satisfy the equations of the so called Minimal Geometric Deformation approach. Namely, we study if they can be seen as a geometric deformation - due to the Brans-Dicke scalar - of the Schwarzschild solution. Indeed, the peculiar feature of the geometric deformation is that it is built in such a way to guarantee a clear limit to the vacuum equations of General Relativity. However, we find that the Brans solutions do not meet all the requirements imposed by the structure of the Minimal Geometric Deformation approach. This result supports the conclusion that there is no simple limiting procedure in which the complete Brans-Dicke theory just reduces to General Relativity.
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Ruscelli, Francesco. "On the Palatini formulation of general relativity." Bachelor's thesis, Alma Mater Studiorum - Università di Bologna, 2021. http://amslaurea.unibo.it/23693/.
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In questo lavoro presentiamo la formulazione di Palatini della Relatività Generale. Per fare ciò, discutiamo le nozioni di base della teoria delle varietà differenziabili e della geometria (pseudo-)Riemanniana. In particolare, ci concentriamo sui fibrati vettoriali e sul concetto di connessione. Quest'ultimo è analizzato sia nel caso particolare di una connessione affine, ovvero sul fibrato tangente ad una varietà, sia nel caso generale di una connessione su un fibrato vettoriale arbitrario.
Mentre la geometria Riemanniana e la Relatività Generale sono state storicamente sviluppate attraverso il calcolo tensoriale, noi seguiamo l'approccio di cui Elie Cartan, nel XX secolo, fu pioniere. Questo approccio individua le forme differenziali come oggetti fondamentali della teoria e risulta fondamentale nella costruzione dell'azione di Palatini. Di conseguenza, dedichiamo ampio spazio alla descrizione della connessione come forma differenziale, insieme alle forme di curvatura e di torsione.
Prima di introdurre il formalismo di Palatini, richiamiamo brevemente le idee fisiche che hanno ispirato la Relatività Generale, come il Principio di Equivalenza, e mostriamo come si possano estrapolare le equazioni di Einstein a partire dall'equazione di Poisson per il potenziale gravitazionale. Infine, utilizziamo il formalismo di Cartan per derivare l'azione di Palatini e mostriamo come dalla variazione di quest'ultima sia possibile ritrovare le equazioni di Einstein.
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Roy, Ian M. "Projective and Ricci collineations in general relativity." Thesis, University of Aberdeen, 1998. http://digitool.abdn.ac.uk/R?func=search-advanced-go&find_code1=WSN&request1=AAIU099861.
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The thesis considers various problems in general relativity concerning projective and Ricci collineations. A result due to Yano in the maximum dimension of the projective algebra on a non-flat space-time is improved using a pointwise classification scheme. The converse of a result, relating Weyl projective vector fields and curvature collineations under certain well defined circumstances, is given. A result is presented showing that, under specified conditions a space-time admitting a proper special projective vector field admits a proper special conformal vector field and vice versa. The work done on Ricci/Matter collineations gives a general mathematical treatment of these vector fields where particular emphasis is placed on decomposable space-times. Problems of differentiability, extendibility, etc are described.
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MacNay, Lucy E. K. "Sectional curvature and symmetry in general relativity." Thesis, University of Aberdeen, 2006. http://digitool.abdn.ac.uk/R?func=search-advanced-go&find_code1=WSN&request1=AAIU224715.
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This thesis contains two main areas of research in General Relativity Theory. These are the study of the sectional curvature function in general relativity and the study of symmetries. The sectional curvature function is a real-valued map defined on the set of all non-null 2-spaces at a certain point in the space-time. several results relating to the sectional curvature function will be given. The bivector curvature function will then be defined as the extension of the sectional curvature function to the set of all "non-null" bivectors at a point in the space-time. Two important results relating to this function will be proved. Symmetries in general relativity have been widely researched. In this thesis, three results on symmetries will be proved. Firstly, it will be shown that there exists a space-time admitting a finite-dimensional curvature collineation algebra not equal to the affine algebra. Then a result on the conformal algebra in a 2-dimensional manifold will be given. Lastly, a proof will be given on the dimension of the sectional curvature preserving algebra.
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Rendall, Alan D. "Some aspects of curvature in general relativity." Thesis, University of Aberdeen, 1987. http://digitool.abdn.ac.uk/R?func=search-advanced-go&find_code1=WSN&request1=AAIU009831.
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The purpose of this thesis is to study in depth the relationship between the curvature of space-time and the other geometrical objects which naturally arise in general relativity. Most of the results obtained apply to the generic case. Chapter 1 contains a discussion of certain aspects of fibre bundle theory required in later chapters which may be unfamiliar to many relativists, while chapter 2 contains preliminary material on curvature in relativity and proves a continuity property of the algebraic classification of the Weyl and energy-momentum tensors. Chapter 3 describes the generic behaviour of the Riemann, Weyl and energy-momentum tensors, and chapter 5 goes on to use this description to investigate the relationship of the Riemann tensor to the metric, conformal class and connection of space-time in the generic case. In particular it is proved that the Riemann tensor uniquely and continuously determines the connections. The information obtained in chapter 3 on the algebraic type of curvature in the general case is related in chapter 4 to the topology of the underlying manifold. In chapter 6 a topology is defined on the set of sectional curvatures of all Lorentz metrics on a given manifold. The remainder of the chapter attempts to do for the sectional curvature what was done for the Riemann tensor in chapter 5 but, because sectional curvature is more difficult to handle, the results obtained are necessarily more modest.
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Eichmair, Michael. "Non-variational existence problems in general relativity /." May be available electronically:, 2008. http://proquest.umi.com/login?COPT=REJTPTU1MTUmSU5UPTAmVkVSPTI=&clientId=12498.
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Cooney, Alan James. "Astrophysical Tests of Gravity Beyond General Relativity." Diss., The University of Arizona, 2013. http://hdl.handle.net/10150/294014.
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The General theory of Relativity (GR) brought gravity into accord with the principles of locality and relativity. Since its discovery it has been preeminent, recognized as the most accurate description of gravity on the many scales where it has been tested. During this period, seemingly radical predictions like the existence of black holes and the expansion of the Universe have been verified and testify to the great leap of insight that GR represented in our understanding of space and time. However not all precision observations of astrophysical systems have yielded easily to interpretation within GR, and with the discovery of cosmic acceleration, there is genuine concern that General Relativity may be incomplete when describing the Universe on the largest sizes imaginable. In this uncertainty, many theoretical models have been proposed. In this thesis we shall first outline the motivation behind a certain subset of these models and the known issues that arise in interpreting these models as alternative theories of gravity. Then focus on one variety of theory the f(R) modifications to gravity. Demonstrating that many of the known instabilities have a common origin and that they are avoided when treating these theories via perturbative constraints. In the second part of this work we examine the astrophysical impact of modifications to gravity, first in the case of high mass neutron stars, then subsequently on corrections to the line profile of neutral hydrogen from violations of the equivalence principle. Finally we explore the phenomenology of modifications to gravity that produce late-Universe acceleration. In particular, what solutions are allowed and what range of accelerations are predicted as a result. Furthermore we explore how a correction to gravity at large scales would impact the growth and evolution of cosmological perturbations.
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Vitagliano, Vincenzo. "Gravity beyond general relativity : theory and phenomenology." Doctoral thesis, SISSA, 2011. http://hdl.handle.net/20.500.11767/4681.
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Despite the notorious achievements of General Relativity, Einstein's theory is under scrutiny due to the lack of a suitable scheme to quantize gravity as well as for the puzzling features it shows both at strong (early universe, black holes) and weak (Dark Energy problem) regime. The proposal to extend the classical theory of gravity harbours the intriguing goals to cure some of these inconsistencies. A large class of modi cations of General Relativity (GR) has been widely explored in the past; in principle, the main motivation for such early e orts was to solve the problem of non-renormalizability by providing a new framework in which (thanks to higher order corrections in the gravitational action) gravity could be quantized. The analysis of the cosmological implications of such models also showed a number of peculiar features that justi ed further developments. The ultraviolet modi cations that naturally arise at high energy in the context of quantum gravity have been taken into account for their impact on the phenomenology of the very early universe. Furthermore, it was recently argued that alternative infrared extensions of the Einstein-Hilbert (EH) action could be invoked to presumably alleviate the Dark Sector problem.
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Webster, Paul S. "Black holes and radiative fields in general relativity." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2000. http://www.collectionscanada.ca/obj/s4/f2/dsk2/ftp03/NQ49548.pdf.
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Mena, Filipe Artur Pacheco Neves Carteado. "Inhomogeneous and anisotropic space times in general relativity." Thesis, Queen Mary, University of London, 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.252193.
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Piper, Matthew Sebastian. "Power series and computer algebra in general relativity." Thesis, Queen Mary, University of London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.264988.
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Keane, Aidan J. "Liouville's equation and radiative acceleration in general relativity." Thesis, University of Glasgow, 1999. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.301358.
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Hossack, Andrew D. "Sectional curvature and plane waves in general relativity." Thesis, University of Aberdeen, 1992. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.314609.
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This thesis considers several problems in general relativity which involve the sectional curvature function σ. The causal structure defined by Lorentzian metrics on space-times makes the behaviour of σ more interesting in general relativity than in classical (positive-definite) geometry and comparisons between results in classical and Lorentzian geometry are made which illustrate this point. The thesis as a whole emphasises the geometrical rather than the physical aspects of the theory. There are three principal areas of study contained in this thesis: A theorem by J.L. Synge which relates sectional and Gaussian curvature along geodesics in classical geometry is introduced and generalised to Lorentzian geometry in a straight-forward manner. A result due to J. Beem and P. Parker concerning the existence of non-destructive null directions (along which gravitational tidal accelerations are bounded), in vacuum space-times is extended to arbitrary space-times in an elegant way. It is known that if a sectional curvature function σ is specified on a manifold then it is possible for two distinct, conformally-related generalised plane wave metrics to both give rise to σ. To investigate those symmetries of these space-times that might preserve σ, the concept of a sectional curvature preserving vector field on these plane waves is introduced and it is shown that these vector fields form a subalgebra of the conformal Lie algebra. A basis of this conformal algebra is then computed and used to establish conditions under which non-trivial sectional curvature preserving vector fields may exist. Other subsidiary results are also obtained as a consequence of these investigations.
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Wilson, Jonathan Peter. "Regularity of axisymmetric space-times in general relativity." Thesis, University of Southampton, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.243657.
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Hayward, Sean A. "The collision of plane waves in general relativity." Thesis, University of Southampton, 1990. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.293211.
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Nahmad-Achar, E. "Angular momentum and metric perturbations in general relativity." Thesis, University of Cambridge, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.382639.
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Keir, Joseph. "Aspects of stability and instability in general relativity." Thesis, University of Cambridge, 2016. https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.709537.
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Kotze, Jacques. "An introduction to general relativity and entropy bounds." Thesis, Stellenbosch : University of Stellenbosch, 2006. http://hdl.handle.net/10019.1/17375.
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Thesis (MSc)--University of Stellenbosch, 2006.ENGLISH ABSTRACT: Entropy bounds arise from Black hole thermodynamics and are a significant departure from the conventional understanding of the information in a given region. This shift in paradigm is a consequence of the the fact that there is an unexpected relationship between the area and the entropy of a given region of spacetime. Entropy bounds are simplified formulations which are ultimately attempting to be developed into the complete and broad conjecture of the Holographic Principle. This hasn’t been achieved successfully as yet. In this thesis the aim is to introduce how the notion of an entropy bound was first suggested and it’s subsequent development into more robust formulations. The shortcomings of these conjectures are highlighted along with their strengths. A foundational introduction of the mathematical requirements for General Relativity is addressed along with an overview of Einstein’s theory of gravity. This is illustrated by showing the curvature of relative geodesics as being a consequence of gravity. This is contrasted with Newtonian theory where gravity is also shown to manifests as the curvature of relative geodesics. The working background is concluded with a discussion of Einstein’s field equations along with simple and common solutions often used and required.
AFRIKAANSE OPSOMMING: Swartgat Termodinamika impliseer grense op die entropie, en dus inligting, in ’n gegewe ruimtetyd volume, wat ’n drastiese afwyking van die tradisionele denkwyse oor inligting impliseer. Hierdie paradigma skuif het sy oorsprong in ’n onverwagte verband tussen die oppervlakte van, en entropie bevat, in ’n gegewe ruimte tyd volume. Entropie grense is eenvoudige formulerings van hierdie verwantskap wat uiteindelik beslag moet kry in die vollediger en wyer holografiese beginsel. Hierdie doelwit is nog nie bereik nie. Die doel van hierdie tesis is om die oorsprong en verdere formalisering van entropie grense te verduidelik. Beide die sterk en swak punte van die formulerings word bespreek. Algemene relatiwiteits teorie as ’n teorie van gravitasie, sowel as die wiskundige onderbou daarvan, word oorsigtelik bespreek. Die geometries onderbou van gravitasie word geillustreer aan die hand van die buiging van relatiewe geodete. Dit word met Newton se gravitasie teorie vergelyk wat ook in die buiging van relatiewe geodete gemanifesteer word. Hierdie oorsigtelike agtergrond word afgesluit met ’n oorsig van Einstein se vergelykings, asook eenvoudige en algemene oplossings wat dikwels nodig is en gebruik word.
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Sylvester, Alex J. "Testing General Relativity with Spherical Resonant Mass Detectors." Thesis, University of Louisiana at Lafayette, 2016. http://pqdtopen.proquest.com/#viewpdf?dispub=10002423.
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Gravitational waves in f(R) gravity excite monopole and m = 0±2 quadrupole resonance modes of a spherical detector. This document reviews the basic ideas of general relativity and gravitational waves, and then applies those concepts to an f( R) gravitational wave. The acoustic response of a GW incident with a spherical detector is reviewed in detail, and the absorption cross section for an f(R) GW impinging on the spherical detector is calculated. Minimum detectable scalar wave amplitudes are explored for the Mario Schenberg detector. The mass of the scalar mode affects its detectability.
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Dorkenoo, Leggat Alasdair. "Dirac solitons in general relativity and conformal gravity." Thesis, University of St Andrews, 2017. http://hdl.handle.net/10023/12127.
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Static, spherically-symmetric particle-like solutions to the coupled Einstein-Dirac and Einstein-Dirac-Maxwell equations have been studied by Finster, Smoller and Yau (FSY). In their work, FSY left the fermion mass as a parameter set to ±1. This thesis generalises these equations to include the Higgs field, letting the fermion mass become a function through coupling, μ. We discuss the dynamics associated with the Higgs field and find that there exist qualitatively similar solutions to those found by FSY, with well behaved, non-divergent metric components and electrostatic potential, close to the origin, going over to the point-particle solutions for large r; the Schwarzschild or Reissner-Nordström metric, and the Coulomb potential. We then go on to discuss an alternative gravity theory, conformal gravity, (CG), and look for solutions of the CG equations of motion coupled to the Dirac, Higgs and Maxwell equations. We obtain asymptotically nonvanishing, yet fully normalisable Dirac spinor components, resembling those of FSY, and, in the case where charge is included, non-divergent electrostatic potential close to the origin, matching onto the Coulomb potential for large r.
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Ida, Daisuke. "FOUNDATION OF MANY-SHELL SYSTEM IN GENERAL RELATIVITY." 京都大学 (Kyoto University), 2001. http://hdl.handle.net/2433/86463.
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