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Trous Noirs PhantomesRodrigues, Manuel 14 April 2010 (has links) (PDF)
We obtain the general solution of the Einstein-(anti) Maxwell-(anti) Dilaton (EMD) theory for a static, spherically symmetric spacetime in four dimensions. In the phantom (anti) cases, we obtain new solutions with non-degenerate horizon and make the analysis of their causal structures. The causal structures of some solutions are exotics, some of them can not be described in two-dimensional usual Penrose diagrams. We obtain also, using the method of Sigma model, new stationary solutions with axial symmetry, for Einstein-anti-Maxwell-Dilaton (EM¯\bar{M}D) and Einstein-anti-Maxwell-Dilaton-Axion (EM¯\bar{M}DA) theory. We analyse the causal structure of these new solutions.
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Computer aided instruction of special relativityLin, Yinghua January 1991 (has links)
This thesis creates an small expert system that is based on Einstein's special relativity. The basic knowledge of special relativity and the bases for building an expert system are described. The concepts of special relativity are put into a knowledge base by changing the formulas into rules and facts. The Prolog language was used to develop the expert system. New information can be input that does not contradict the rules and facts already in the database. The system also uses computer graphics to demonstrate the physical concepts of relativity. By using this expert system, one can teach the basic knowledge of special relativity and solve some problems related to frames of reference moving with high speed. / Department of Computer Science
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Black Hole Formation in Lovelock GravityTaves, Timothy Mark January 2012 (has links)
Some branches of quantum gravity demand the existence of higher dimensions and the addition of higher curvature terms to the gravitational Lagrangian in the form of the Lovelock polynomials. In this thesis we investigate some of the classical properties of Lovelock gravity.
We first derive the Hamiltonian for Lovelock gravity and find that it takes the same form as in general relativity when written in terms of the Misner-Sharp mass function. We then minimally couple the action to matter fields to find Hamilton’s equations of motion. These are gauge fixed to be in the Painleve-Gullstrand co–ordinates and are well suited to numerical studies of black hole formation.
We then use these equations of motion for the massless scalar field to study the formation of general relativistic black holes in four to eight dimensions and Einstein-Gauss-Bonnet black holes in five and six dimensions. We study Choptuik scaling, a phenomenon which relates the initial conditions of a matter distribution to the final observables of small black holes.
In both higher dimensional general relativity and Einstein-Gauss-Bonnet gravity we confirm the existence of cusps in the mass scaling relation which had previously only been observed in four dimensional general relativity. In the general relativistic case we then calculate the critical exponents for four to eight dimensions and find agreement with previous calculations by Bland et al but not Sorkin et al who both worked in null co–ordinates.
For the Einstein-Gauss-Bonnet case we find that the self-similar behaviour seen in the general relativistic case is destroyed. We find that it is replaced by some other form of scaling structure. In five dimensions we find that the period of the critical solution at the origin is proportional to roughly the cube root of the Gauss-Bonnet parameter and that there is evidence for a minimum black hole radius. In six dimensions we see evidence for a new type of scaling. We also show, from the equations of motion, that there is reason to expect qualitative differences between five and higher dimensions.
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Applications of embedding theory in higher dimensional general relativity.Moodley, Jothi. 22 April 2014 (has links)
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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Spherically symmetric solutions in relativistic astrophysics.John, Anslyn James. January 2002 (has links)
In this thesis we study classes of static spherically symmetric spacetimes admitting a perfect
fluid source, electromagnetic fields and anisotropic pressures. Our intention is to generate
exact solutions that model the interior of dense, relativistic stars. We find a sufficient
condition for the existence of series solutions to the condition of pressure isotropy for neutral
isolated spheres. The existence of a series solution is demonstrated by the method of
Frobenius. With the help of MATHEMATICA (Wolfram 1991) we recovered the Tolman
VII model for a quadratic gravitational potential, but failed to obtain other known classes
of solution. This establishes the weakness, in certain instances, of symbolic manipulation
software to extract series solutions from differential equations. For a cubic potential, we
obtained a new series solution to the Einstein field equations describing neutral stars. The
gravitational and thermodynamic variables are non-singular and continuous. This model also
satisfies the important barotropic equation of state p = p(p). Two new exact solutions to
the Einstein-Maxwell system, that generalise previous results for uncharged stars, were also
found. The first of these generalises the solution of Maharaj and Mkhwanazi (1996), and has
well-behaved matter and curvature variables. The second solution reduces to the Durgapal
and Bannerji (1983) model in the uncharged limit; this new result may only serve as a toy
model for quark stars because of negative energy densities. In both examples we observe that
the solutions may be expressed in terms of hypergeometric and elementary functions; this
indicates the possibility of unifying isolated solutions under the hypergeometric equation.
We also briefly study compact stars with spheroidal geometry, that may be charged or admit
anisotropic pressure distributions. The adapted forms of the pressure isotropy condition can
be written as a harmonic oscillator equation. Two simple examples are presented. / Thesis (M.Sc.)-University of Natal, Durban, 2002.
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Quantum Field Theory: Motivating the Axiom of MicrocausalityWright, Jessey January 2012 (has links)
Axiomatic quantum field theory is one approach to the project of merging the special theory of relativity with that of ordinary quantum mechanics. The project begins with the postulation of a set of axioms. Axioms should be motivated by reasonable physical principles in a way that illustrates how a given axiom is true. Motivations are often grounded in the principles of the parent theories: ordinary quantum mechanics or the theory of special relativity. Amongst the set of axioms first proposed by Haag and Kastler in 1963 is the axiom of microcausality. Microcausality requires the observables of regions at space-like separation to commute. This thesis seeks to answer the question ‘What principles from the special theory of relativity or ordinary quantum mechanics motivate, or justify, accepting microcausality as an axiom?’ The first chapter will provide the necessary background to investigate this question and the second chapter will undertake that investigation. In conclusion, microcausality cannot be well-motivated by individual principles rooted in the special theory of relativity or ordinary quantum mechanics.
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Higher Dimensional Gravity, Black Holes and Brane WorldsCarter, Benedict Miles Nicholas January 2006 (has links)
Current research is focussed on extending our knowledge of how gravity behaves on small scales and near black hole horizons, with various modifications which may probe the low energy limits of quantum gravity. This thesis is concerned with such modifications to gravity and their implications. In chapter two thermodynamical stability analyses are performed on higher dimensional Kerr anti de Sitter black holes. We find conditions for the black holes to be able to be in thermal equilibrium with their surroundings and for the background to be stable against classical tensor perturbations. In chapter three new spherically symmetric gravastar solutions, stable to radial perturbations, are found by utilising the construction of Visser and Wiltshire. The solutions possess an anti de Sitter or de Sitter interior and a Schwarzschild (anti) de Sitter or Reissner Nordstrom exterior. We find a wide range of parameters which allow stable gravastar solutions, and present the different qualitative behaviors of the equation of state for these parameters. In chapter four a six dimensional warped brane world compactification of the Salam-Sezgin supergravity model is constructed by generalizing an earlier hybrid Kaluza Klein / Randall Sundrum construction. We demonstrate that the model reproduces localized gravity on the brane in the expected form of a Newtonian potential with Yukawa type corrections. We show that allowed parameter ranges include values which potentially solve the hierarchy problem. The class of solutions given applies to Ricci flat geometries in four dimensions, and consequently includes brane world realisations of the Schwarzschild and Kerr black holes as particular examples. Arguments are given which suggest that the hybrid compactification of the Salam Sezgin model can be extended to reductions to arbitrary Einstein space geometries in four dimensions. This work furthers our understanding of higher dimensional general relativity, which is potentially interesting given the possibility that higher dimensions may become observable at the TeV scale, which will be probed in the Large Hadron Collider in the next few years.
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Some effects of spacetime curvature in general relativity /McClune, James C. January 1997 (has links)
Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references. Also available on the Internet.
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Some effects of spacetime curvature in general relativityMcClune, James C. January 1997 (has links)
Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references. Also available on the Internet.
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Tests of the Aharonov-Bohm effectCaprez, Adam Preston. January 2009 (has links)
Thesis (Ph.D.)--University of Nebraska-Lincoln, 2009. / Title from title screen (site viewed June 26, 2009). PDF text: x, 153 p. : ill. (some col.) ; 9 Mb. UMI publication number: AAT 3350442. Includes bibliographical references. Also available in microfilm and microfiche formats.
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