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On Stephani universes.Moopanar, Selvandren. January 1992 (has links)
In this dissertation we study conformal symmetries in the Stephani universe which is
a generalisation of the Robertson-Walker models. The kinematics and dynamics of
the Stephani universe are discussed. The conformal Killing vector equation for the
Stephani metric is integrated to obtain the general solution subject to integrability
conditions that restrict the metric functions. Explicit forms are obtained for the
conformal Killing vector as well as the conformal factor . There are three categories
of solution. The solution may be categorized in terms of the metric functions k and
R. As the case kR - kR = 0 is the most complicated, we provide all the details of
the integration procedure. We write the solution in compact vector notation. As the
case k = 0 is simple, we only state the solution without any details. In this case
we exhibit a conformal Killing vector normal to hypersurfaces t = constant which is
an analogue of a vector in the k = 0 Robertson-Walker spacetimes. The above two
cases contain the conformal Killing vectors of Robertson-Walker spacetimes. For
the last case in - kR = 0, k =I 0 we provide an outline of the integration process.
This case gives conformal Killing vectors which do not reduce to those of RobertsonWalker
spacetimes. A number of the calculations performed in finding the solution
of the conformal Killing vector equation are extremely difficult to analyse by hand.
We therefore utilise the symbolic manipulation capabilities of Mathematica (Ver 2.0)
(Wolfram 1991) to assist with calculations. / Thesis (M.Sc.)-University of Natal, Durban, 1992.
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Aspects of spherically symmetric cosmological models.Moodley, Kavilan. January 1998 (has links)
In this thesis we consider spherically symmetric cosmological models when the shear
is nonzero and also cases when the shear is vanishing. We investigate the role of
the Emden-Fowler equation which governs the behaviour of the gravitational field.
The Einstein field equations are derived in comoving coordinates for a spherically
symmetric line element and a perfect fluid source for charged and uncharged matter.
It is possible to reduce the system of field equations under different assumptions to
the solution of a particular Emden-Fowler equation. The situations in which the
Emden-Fowler equation arises are identified and studied. We analyse the Emden-Fowler
equation via the method of Lie point symmetries. The conditions under which
this equation is reduced to quadratures are obtained. The Lie analysis is applied to
the particular models of Herlt (1996), Govender (1996) and Maharaj et al (1996) and
the role of the Emden-Fowler equation is highlighted. We establish the uniqueness
of the solutions of Maharaj et al (1996). Some physical features of the Einstein-Maxwell
system are noted which distinguishes charged solutions. A charged analogue
of the Maharaj et al (1993) spherically symmetric solution is obtained. The Gutman-Bespal'ko
(1967) solution is recovered as a special case within this class of solutions
by fixing the parameters and setting the charge to zero. It is also demonstrated
that, under the assumptions of vanishing acceleration and proper charge density,
the Emden-Fowler equation arises as a governing equation in charged spherically
symmetric models. / Thesis (M.Sc.)-University of Natal, Durban, 1998.
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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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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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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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Computational and astrophysical studies of black hole spacetimesBonning, Erin Wells, Matzner, Richard A. January 2004 (has links) (PDF)
Thesis (Ph. D.)--University of Texas at Austin, 2004. / Supervisor: Richard Matzner. Vita. Includes bibliographical references. Available also from UMI company.
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Initial data for black holes and rough spacetimes /Maxwell, David A. January 2004 (has links)
Thesis (Ph. D.)--University of Washington, 2004. / Vita. Includes bibliographical references (p. 90-94).
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